Question

Answer with the explanation step by step

Answer 1

The answer is A.
`(3(x-21))/((x+7)(x-7))`.

Explanation:

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

Then, simplify the terms in the problem by first multiplying
`(3)/(x+7)` and
`(x-7)/(x-7)`, which will look like
`(3(x-7))/((x+7)(x-7))-(42)/((x+7)(x-7))`. The next step is to combine the numerators over the common denominator, which will look like
`(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
`(3(x-7-14))/((x+7)(x-7))`. Then, subtract 14 from -7, which will look like
`(3(x-21))/((x+7)(x-7))`. The final answer will be
`(3(x-21))/((x+7)(x-7))`.