Question

Answer with the explanation step by step

Answer 1

Answer:

The answer is A. $\frac{3(x-21)}{(x+7)(x-7)}$.

Step-by-step explanation:

To find the difference of this problem, start by simplifying the denominator, which will look like $\frac{3}{x+7}-\frac{42}{(x+7)(x-7)}$. Next, multiply $\frac{3}{x+7}$ by $\frac{x-7}{x-7}$  to create a fraction with a common denominator in order to subtract from $\frac{42}{(x+7)(x-7)}$. The problem will now look like $\frac{3}{x+7}*\frac{x-7}{x-7}-\frac{42}{(x+7)(x-7)}$.  

Then, simplify the terms in the problem by first multiplying $\frac{3}{x+7}$ and $\frac{x-7}{x-7}$, which will look like $\frac{3(x-7)}{(x+7)(x-7)}-\frac{42}{(x+7)(x-7)}$. The next step is to combine the numerators over the common denominator, which will look like $\frac{3(x-7)-42}{(x+7)(x-7)}$.

Next, simplify the numerator, and to simplify the numerator start by factoring 3 out of $3(x-7)-42$, which will look like $\frac{3(x-7-14)}{(x+7)(x-7)}$. Then, subtract 14 from -7, which will look like $\frac{3(x-21)}{(x+7)(x-7)}$. The final answer will be $\frac{3(x-21)}{(x+7)(x-7)}$.