Maths-
General
Easy

Question

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

hintHint:

Simplify means to make it simple. In mathematics, simplify is the reduction of an expression/fraction into irreducible forms. The product of two expressions is the result of multiplying them.
We are asked to find the product of the expressions.

The correct answer is: To find the domain of the expression, find the values, for which the denominator takes a zero value, ( x - 7 ) = 0 x = 7


    Step 1 of 3:
    Simplify the expression, fraction numerator 3 x squared plus 6 x over denominator x squared minus 49 end fractionusing the identity,open parentheses x squared minus a squared close parentheses equals left parenthesis x minus a right parenthesis left parenthesis x plus a right parenthesis
    fraction numerator 3 x squared plus 6 x over denominator x squared minus 49 end fraction equals fraction numerator 3 x left parenthesis x plus 2 right parenthesis over denominator open parentheses x squared minus 7 squared close parentheses end fraction
    equals fraction numerator 3 x left parenthesis x plus 2 right parenthesis over denominator left parenthesis x minus 7 right parenthesis left parenthesis x plus 7 right parenthesis end fraction
    Simplify the expression, open parentheses x squared plus 9 x plus 14 close parentheses, using the identityleft parenthesis x plus a right parenthesis left parenthesis x plus b right parenthesis equals x squared plus left parenthesis a plus b right parenthesis x plus a b
    open parentheses x squared plus 9 x plus 14 close parentheses equals x squared plus 7 x plus 2 x plus 14
    equals x left parenthesis x plus 7 right parenthesis plus 2 left parenthesis x plus 7 right parenthesis
    equals left parenthesis x plus 2 right parenthesis left parenthesis x plus 7 right parenthesis
    Step 2 of 3:
    Find the product of the simplified expression,
    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 equals fraction numerator 3 x left parenthesis x plus 2 right parenthesis over denominator left parenthesis x minus 7 right parenthesis left parenthesis x plus 7 right parenthesis end fraction cross times left parenthesis x plus 2 right parenthesis left parenthesis x plus 7 right parenthesis
    equals fraction numerator 3 x left parenthesis x plus 2 right parenthesis squared over denominator left parenthesis x minus 7 right parenthesis end fraction
    Step 3 of 3:
    To find the domain of the expression, find the values, for which the denominator takes a zero value,
    left parenthesis x minus 7 right parenthesis equals 0
    x equals 7
    Thus, the domain is:
    left parenthesis negative straight infinity comma 7 right parenthesis union left parenthesis 7 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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