Question

If no denominator equals zero, which expression is equivalent to ? A. B. C. D.

Answer 1

The expression $\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}$ is equivalent to  $\dfrac{22x+48}{x^2-36}$  and it can be determined by using LCM and fraction.

Given that,

Expression;

$\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}$

If no denominator equals zero,

We have to determine,

Which expression is equivalent to the given expression?

According to the question,

Expression;

$\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}$

If no denominator equals zero,

To determine the equivalent relation of the given equation following all the steps given below.

• Step1; First take the LCM,

                   $\rm= \dfrac{15}{x-6}+\dfrac{7}{x+6}\\\\=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}$

• Step2; Multiply the terms and simplify the equation,

                   $\rm=\dfrac{15(x+6) + 7(x-6)}{(x-6) (x+6)}\\\\= \dfrac{15x+90 + 7x-42}{x(x+6) -6 (x+6)}\\\\= \dfrac{22x+48}{x^2+6x -6 x-36}\\\\= \dfrac{22x+48}{x^2-36}$

Hence, The expression $\rm \dfrac{15}{x-6}+\dfrac{7}{x+6}$ is equivalent to  $\dfrac{22x+48}{x^2-36}$ .

For more details about Expression refer to the link given below.

brainly.com/question/14610993