Reduce the following rational expressions to their lowest terms
$fraction numerator 8 x to the power of 5 minus 8 x over denominator open parentheses 3 x squared plus 3 close parentheses left parenthesis 4 x plus 4 right parenthesis end fraction$

The LCM of the polynomials $5 open parentheses x squared minus 2 x close parentheses left parenthesis x minus 6 right parenthesis squared straight & 2 x open parentheses x squared minus 4 close parentheses left parenthesis x minus 6 right parenthesis squared$ is.

Write the equation in slope-intercept form of the line that passes through the points (5, 4) and (-1, 6).

The slope intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. We can draw the graph of a linear equation on the x-y coordinate plane using this form of a linear equation.
Steps for determining a line's equation from two points:
Step 1: The slope formula used to calculate the slope.
Step 2: To determine the y-intercept, use the slope and one of the points (b).
Step 3: Once you know the values for m and b, we can plug them into the slope-intercept form of a line, i.e., (y = mx + b), to obtain the line's equation.

Write the equation in slope-intercept form of the line that passes through the points (5, 4) and (-1, 6).

What is the simplified form of the rational expressions ? What is the domain for which the identity between the two expressions is valid ?
$fraction numerator x cubed minus 5 x squared minus 24 x over denominator x cubed plus x squared minus 72 x end fraction$

Explain $fraction numerator 4 x squared minus 7 over denominator 4 x squared minus 7 end fraction$ =1 why is a valid identity under the domain of all real numbers except $plus-or-minus fraction numerator square root of 7 over denominator 2 end fraction$ .

The HCF of the polynomials $open parentheses x squared minus 2 x plus 1 close parentheses left parenthesis x plus 4 right parenthesis straight & open parentheses x squared plus 3 x minus 4 close parentheses left parenthesis x plus 1 right parenthesis$ is:

simplify $fraction numerator 81 x to the power of 4 minus 16 x squared plus 32 x minus 16 over denominator 9 x squared minus 4 x plus 4 end fraction$

When are two rational expressions equivalent? Explain with an example.

Sketch the graph of $y equals negative 3 over 4 x minus 5$

If the LCM of f(x) and g(x) is $a to the power of 6 minus b to the power of 6$ , then their HCF can be ________.

Create a flow chart to show the process to determine whether a given data set represents a function that is linear , quadratic , exponential or none of these.

Solve for $cube root of 5 x end root equals 25$

A Company’s profit from a certain product is represented by p(x)= -5x²+1 , 125x-5000, where x is the price of the product . Compare the growth in profits from x= 120 to 140 and from x= 140 to 160 , What do you notice ?

$3 square root of x plus 22 end root equals 21$ Solve for x

The formula $d equals fraction numerator square root of 15 W end root over denominator 3.14 end fraction$ gives the diameter d, in inches, of a rope needed to lift a weight of w, intons. How much weight can be lifted with a rope that has a diameter of 4in?