Maths-
General
Easy

Question

Find the simplified Quotient and the domain of each expression
fraction numerator 2 x squared minus 12 x over denominator x plus 5 end fraction divided by fraction numerator x minus 6 over denominator x plus 5 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: The simplified expression is2x ,which is a polynomial. Hence, the domain is the set of real numbers,


    Step 1 of 3:
    The given expression is:fraction numerator 2 x squared minus 12 x over denominator x plus 5 end fraction divided by fraction numerator x minus 6 over denominator x plus 5 end fraction
    Write the reciprocal of the second expression and then multiply them together;
    fraction numerator 2 x squared minus 12 x over denominator x plus 5 end fraction divided by fraction numerator x plus 5 over denominator x minus 6 end fraction
    Step 2 of 3:
    Simplify the terms of the expression,
    fraction numerator 2 x squared minus 12 x over denominator x plus 5 end fraction cross times fraction numerator x plus 5 over denominator x minus 6 end fraction equals fraction numerator 2 x left parenthesis x minus 6 right parenthesis over denominator x plus 5 end fraction cross times fraction numerator x plus 5 over denominator x minus 6 end fraction
    = 2x
    Step 3 of 3:
    The simplified expression is 2x ,which is a polynomial. Hence, the domain is the set of real numbers,
    left parenthesis negative straight infinity comma straight infinity right parenthesis

    The domain of any polynomial is the set of real numbers.

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