simplify the rational expression completely:

Question

show step by work:

x²-49 ⁄ x²-6x-7

Answer 1

Hi Mona H.

It simplifies to

(x + 7)/ (x + 1)

x²-49 ⁄ x²-6x-7

Factor the numerator and denominator

The numerator is the difference between two perfect squares

x²-49 with factors (x - 7)(x + 7)

The denominator is a quadratic

x²-6x-7 = (x - 7)(x + 1)

And we have

(x - 7)(x + 7)/ (x - 7)(x + 1)

Since (x - 7) is common to the numerator and denominator it cancels out and we have

(x + 7)/ (x + 1)

I hope this helps please send me a message if you have any questions