Question

Which of the following is the product

Answer 1

Answer:

  $\text{\bf{A.}}\quad\dfrac{3x^2}{x^2-6x-7}$

Step-by-step explanation:

As with multiplying any rational expressions, the numerator of the result is the product of the numerators, and the denominator of the result is the product of the denominators.

$\dfrac{3x}{x+1}\cdot\dfrac{x}{x-7}=\dfrac{(3x)(x)}{(x+1)(x-7)}=\dfrac{3x^2}{x^2-6x-7}$

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The denominator product is found using the distributive property. Each of the terms of one factor is multiplied by the other factor.

$(x+1)(x-7)=x(x-7)+1(x-7)\\\\=x^2-7x+1x-7=x^2-6x-7$