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General
Easy

Question

Find the simplified form of each product , and give the domain.
fraction numerator x plus 3 over denominator 4 x end fraction cross times fraction numerator 3 x minus 18 over denominator 6 x plus 18 end fraction cross times fraction numerator x squared over denominator 4 x plus 12 end fraction

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 simplified form of the product and its domain.

The correct answer is: The value for which the domain of the expression attains a zero value is: 32( x + 3 ) = 0 x + 3 = 0 x = - 3


    Step 1 of 2:
    Simplify the numerator of the expression;
    fraction numerator x plus 3 over denominator 4 x end fraction cross times fraction numerator 3 x minus 18 over denominator 6 x plus 18 end fraction cross times fraction numerator x squared over denominator 4 x plus 12 end fraction equals fraction numerator x plus 3 over denominator 4 x end fraction cross times fraction numerator 3 left parenthesis x minus 6 right parenthesis over denominator 6 x plus 18 end fraction cross times fraction numerator x squared over denominator 4 x plus 12 end fraction
    Now, simplify the denominator;
    fraction numerator x plus 3 over denominator 4 x end fraction cross times fraction numerator 3 left parenthesis x minus 6 right parenthesis over denominator 6 x plus 18 end fraction cross times fraction numerator x squared over denominator 4 x plus 12 end fraction equals fraction numerator x plus 3 over denominator 4 x end fraction cross times fraction numerator 3 left parenthesis x minus 6 right parenthesis over denominator 6 left parenthesis x plus 3 right parenthesis end fraction cross times fraction numerator x squared over denominator 4 left parenthesis x plus 3 right parenthesis end fraction
    equals fraction numerator x left parenthesis x minus 6 right parenthesis over denominator 32 left parenthesis x plus 3 right parenthesis end fraction
    Thus, the simplified expression is:equals fraction numerator x left parenthesis x minus 6 right parenthesis over denominator 32 left parenthesis x plus 3 right parenthesis end fraction
    Step 2 of 2:
    The value for which the domain of the expression attains a zero value is:
    32 left parenthesis x plus 3 right parenthesis equals 0
    x plus 3 equals 0
    x equals negative 3
    So, the domain of the expression is:left parenthesis negative straight infinity comma negative 3 right parenthesis union left parenthesis negative 3 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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