Question

Can someone solve this problem thank you

Answer 1

`(3)/(x+7)`

Explanation:

`(3x-21)/(x^(2) -49)`

We will start with factoring the numerator, by pulling a 3 out of each term:

3(x - 7)

We will then factor the denominator. As the denominator is a difference of perfect squares (in the form
`x^(2) -a^(2)`), we know that it can be factored in the form (x + a)(x - a), a being the square root of the number given. (In this case, a = 7, because the square root of 49 is 7.)

Our denominator is now:

(x + 7)(x - 7)

And our fraction is now:

`(3(x-7))/((x-7)(x+7))`

As both the numerator and denominator have the term (x-7), they will cancel, leaving us with the simplified expression:

`(3)/(x+7)`