Maths-
General
Easy

Question

Find the simplified Quotient and the domain of each expression:fraction numerator 1 over denominator x squared plus 9 x end fraction divided by fraction numerator 6 minus x over denominator 3 x squared minus 8 x end fraction
 

hintHint:

To find the quotient is just to divide the expressions. To divide an expression, multiply the first rational expression by the reciprocal of the second rational expression. Domain is the set of input values of an expression.
We are asked to find the quotient and domain of the expression.

The correct answer is: To find the domain, we have to exclude the values for which the denominator of the expression attains a zero value. ( x + 9 ) ( 6 - x ) = 0 x = 6


    Step 1 of 3:
    The given expression is:fraction numerator 1 over denominator x squared plus 9 x end fraction divided by fraction numerator 6 minus x over denominator 3 x squared minus 8 x end fraction
    Write the reciprocal of the second expression and then multiply them together,fraction numerator 1 over denominator x squared plus 9 x end fraction cross times fraction numerator 3 x squared minus 8 x over denominator 6 minus x end fraction
    Step 2 of 3:
    Simplify the terms of the expression in to their simplest form,
    fraction numerator 1 over denominator x squared plus 9 x end fraction cross times fraction numerator 3 x squared minus 8 x over denominator 6 minus x end fraction equals fraction numerator 1 over denominator x left parenthesis x plus 9 right parenthesis end fraction cross times fraction numerator x left parenthesis 3 x minus 8 right parenthesis over denominator 6 minus x end fraction
    equals fraction numerator 1 over denominator left parenthesis x plus 9 right parenthesis end fraction cross times fraction numerator left parenthesis 3 x minus 8 right parenthesis over denominator left parenthesis 6 minus x right parenthesis end fraction
    equals fraction numerator left parenthesis 3 x minus 8 right parenthesis over denominator left parenthesis x plus 9 right parenthesis left parenthesis 6 minus x right parenthesis end fraction
    Step 3 of 3:
    To find the domain, we have to exclude the values for which the denominator of the expression attains a zero value.
    left parenthesis x plus 9 right parenthesis left parenthesis 6 minus x right parenthesis equals 0
    x equals negative 9
    x equals 6
    Thus, the domain of the expression is:
    left parenthesis negative straight infinity comma negative 9 right parenthesis union left parenthesis negative 9 comma 6 right parenthesis union left parenthesis 6 comma straight infinity right parenthesis

    When you find the domain of a rational expression exclude the values that bring zero to the denominator.

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