Maths-
General
Easy

Question

Find the simplified product , and state the domain .
fraction numerator x squared plus x minus 12 over denominator x squared minus x minus 6 end fraction cross times fraction numerator x plus 2 over denominator x plus 4 end fraction

hintHint:

The expansion of the expression left parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis text  is  end text open parentheses x squared plus left parenthesis a plus b right parenthesis x plus a b close parentheses.
We are asked to simplify the product and find the domain.

The correct answer is: the domain is set of real numbers. Even when you substitute any value, to would end up getting the constant value 1.


    Step 1 of 2:
    Simplify the expression and cancel out the common factors;

    fraction numerator x squared plus x minus 12 over denominator x squared minus x minus 6 end fraction cross times fraction numerator x plus 2 over denominator x plus 4 end fraction equals fraction numerator x squared plus 4 x minus 3 x minus 12 over denominator x squared minus 3 x plus 2 x minus 6 end fraction cross times fraction numerator x plus 2 over denominator x plus 4 end fraction

                                                                                    equals fraction numerator x left parenthesis x plus 4 right parenthesis minus 3 left parenthesis x plus 4 right parenthesis over denominator x left parenthesis x minus 3 right parenthesis plus 2 left parenthesis x minus 3 right parenthesis end fraction cross times fraction numerator x plus 2 over denominator x plus 4 end fraction

                                                                                         equals fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis x plus 4 right parenthesis over denominator left parenthesis x plus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction cross times fraction numerator x plus 2 over denominator x plus 4 end fraction

                                                                                                           = 1
    Thus, the simplified expression is 1.
    Step 2 of 2:
    The simplified expression is 1, which is a constant.
    Thus, the domain is set of real numbers. Even when you substitute any value, to would end up getting the constant value 1.

    The domain of a constant number is always the set of real numbers.

    Related Questions to study

    General
    Maths-

    What is the quotient of fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator 1 minus x squared end fraction divided by fraction numerator x squared plus 5 x plus 4 over denominator x squared plus 3 x minus 4 end fraction

    What is the quotient of fraction numerator x cubed plus 3 x squared plus 3 x plus 1 over denominator 1 minus x squared end fraction divided by fraction numerator x squared plus 5 x plus 4 over denominator x squared plus 3 x minus 4 end fraction

    Maths-General
    General
    Maths-

    What is the simplified form of each rational expression ? What is the domain ?
    fraction numerator straight x cubed plus 9 straight x squared minus 10 straight x over denominator straight x cubed minus 9 straight x squared minus 10 straight x end fraction

    What is the simplified form of each rational expression ? What is the domain ?
    fraction numerator straight x cubed plus 9 straight x squared minus 10 straight x over denominator straight x cubed minus 9 straight x squared minus 10 straight x end fraction

    Maths-General
    General
    Maths-

    Write the equation in slope-intercept form of the line that passes through the points (-2, -1) and (0, -5).

    If the slope of the line is to be examined and the given point is also the
    ¶y-intercept, you can apply the slope-intercept formula, y = mx + b. (0, b). The y value of the
    ¶y-intercept point is represented by the symbol b in the formula. If we know the slope between two points on a line, we can use that information to solve for the y-intercept in the slope-intercept equation y=mx+b. Here, we'll develop an equation for the line that connects the points (-1, 6) and (5,-4)

    Write the equation in slope-intercept form of the line that passes through the points (-2, -1) and (0, -5).

    Maths-General

    If the slope of the line is to be examined and the given point is also the
    ¶y-intercept, you can apply the slope-intercept formula, y = mx + b. (0, b). The y value of the
    ¶y-intercept point is represented by the symbol b in the formula. If we know the slope between two points on a line, we can use that information to solve for the y-intercept in the slope-intercept equation y=mx+b. Here, we'll develop an equation for the line that connects the points (-1, 6) and (5,-4)

    parallel
    General
    Maths-

    Find the simplified product , and state the domain
    fraction numerator 8 x plus x squared over denominator x cubed plus 5 x squared minus 24 x end fraction cross times space x cubed plus 2 x squared minus 15 x

    Find the simplified product , and state the domain
    fraction numerator 8 x plus x squared over denominator x cubed plus 5 x squared minus 24 x end fraction cross times space x cubed plus 2 x squared minus 15 x

    Maths-General
    General
    Maths-

    Find the simplified form of each product , and give the domain.
    fraction numerator 3 x squared plus 6 x over denominator x squared minus 49 end fraction cross times open parentheses x squared plus 9 x plus 14 close parentheses

    Find the simplified form of each product , and give the domain.
    fraction numerator 3 x squared plus 6 x over denominator x squared minus 49 end fraction cross times open parentheses x squared plus 9 x plus 14 close parentheses

    Maths-General
    General
    Maths-

    Write the equation in slope-intercept form of the line that passes through the points open parentheses 3 over 8 comma 0 close parentheses straight & open parentheses 5 over 8 comma 1 half close parentheses

    Write the equation in slope-intercept form of the line that passes through the points open parentheses 3 over 8 comma 0 close parentheses straight & open parentheses 5 over 8 comma 1 half close parentheses

    Maths-General
    parallel
    General
    Maths-

    What is the simplified form of each rational expression ? What is the domain ?
    fraction numerator straight x squared plus 8 straight x plus 15 over denominator straight x squared minus straight x minus 12 end fraction

    What is the simplified form of each rational expression ? What is the domain ?
    fraction numerator straight x squared plus 8 straight x plus 15 over denominator straight x squared minus straight x minus 12 end fraction

    Maths-General
    General
    Maths-

    Write the equation in slope-intercept form of the line that passes through the points (-2, -6) and (1, 2).

    Write the equation in slope-intercept form of the line that passes through the points (-2, -6) and (1, 2).

    Maths-General
    General
    Maths-

    Find the simplified Quotient , and state the domain.
    fraction numerator begin display style fraction numerator x squared minus 36 over denominator x squared minus 3 x minus 18 end fraction end style over denominator begin display style fraction numerator x squared plus 2 x minus 24 over denominator x squared plus 7 x plus 12 end fraction end style end fraction

    Find the simplified Quotient , and state the domain.
    fraction numerator begin display style fraction numerator x squared minus 36 over denominator x squared minus 3 x minus 18 end fraction end style over denominator begin display style fraction numerator x squared plus 2 x minus 24 over denominator x squared plus 7 x plus 12 end fraction end style end fraction

    Maths-General
    parallel
    General
    Maths-

    Find the simplified form of each product , and give the domain.
    fraction numerator x cubed minus 4 x over denominator 6 x squared minus 13 x minus 5 end fraction cross times open parentheses 2 x cubed minus 3 x squared minus 5 x close parentheses

    Find the simplified form of each product , and give the domain.
    fraction numerator x cubed minus 4 x over denominator 6 x squared minus 13 x minus 5 end fraction cross times open parentheses 2 x cubed minus 3 x squared minus 5 x close parentheses

    Maths-General
    General
    Maths-

    What is the simplified form of each rational expression ? What is the domain ?
    fraction numerator ab cubed minus 9 ab over denominator 12 ab squared plus 12 ab minus 144 straight a end fraction

    What is the simplified form of each rational expression ? What is the domain ?
    fraction numerator ab cubed minus 9 ab over denominator 12 ab squared plus 12 ab minus 144 straight a end fraction

    Maths-General
    General
    Maths-

    Write the equation in slope-intercept form of the line that passes through the points (4, 0) and (0, 2).

    The slope intercept form is one way to express the line equation y = mx + b. The slope of the line is denoted by m, while the y-intercept is by b. When you want to find a point on a line or solve for y, if you know the value of x, you use the slope-intercept form.
    Y = mx+b
    y = coordinate y
    m = slope
    x = coordinate x
    b = y-intercept
    Given two points on a line, we can write an equation for that line by first determining the slope between those points and then solving for the y-intercept in the slope-intercept equation y = mx + b.

    Write the equation in slope-intercept form of the line that passes through the points (4, 0) and (0, 2).

    Maths-General

    The slope intercept form is one way to express the line equation y = mx + b. The slope of the line is denoted by m, while the y-intercept is by b. When you want to find a point on a line or solve for y, if you know the value of x, you use the slope-intercept form.
    Y = mx+b
    y = coordinate y
    m = slope
    x = coordinate x
    b = y-intercept
    Given two points on a line, we can write an equation for that line by first determining the slope between those points and then solving for the y-intercept in the slope-intercept equation y = mx + b.

    parallel
    General
    Maths-

    Find the simplified Quotient , and state the domain.
    fraction numerator begin display style fraction numerator 2 x squared plus 5 x minus 3 over denominator x squared minus 4 x minus 21 end fraction end style over denominator begin display style fraction numerator 2 x squared plus 5 x minus 3 over denominator 3 x plus 9 end fraction end style end fraction

    Find the simplified Quotient , and state the domain.
    fraction numerator begin display style fraction numerator 2 x squared plus 5 x minus 3 over denominator x squared minus 4 x minus 21 end fraction end style over denominator begin display style fraction numerator 2 x squared plus 5 x minus 3 over denominator 3 x plus 9 end fraction end style end fraction

    Maths-General
    General
    Maths-

    What is the product of fraction numerator x plus 2 over denominator x to the power of 4 minus 16 end fraction straight & x cubed plus 4 x squared minus 12 x.

    What is the product of fraction numerator x plus 2 over denominator x to the power of 4 minus 16 end fraction straight & x cubed plus 4 x squared minus 12 x.

    Maths-General
    General
    Maths-

    What is the simplified form of each rational expression ? What is the domain ?
    fraction numerator straight y squared minus 5 straight y minus 24 over denominator straight y squared plus 3 straight y end fraction

    What is the simplified form of each rational expression ? What is the domain ?
    fraction numerator straight y squared minus 5 straight y minus 24 over denominator straight y squared plus 3 straight y end fraction

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.