How do you simplify (x+5 )/ (x^2-25)?

2 Answers
Jim G.
Jun 22, 2018

1/(x-5)

Explanation:

x^2-25" is a "color(blue)"difference of squares"

a^2-b^2=(a-b)(a+b)

x^2-25=x^2-5^2=(x-5)(x+5)

(cancel((x+5)))/(cancel((x+5))(x-5))=1/(x-5)

"with restriction "x!=5

Jacobi J.
Jun 22, 2018

1/(x-5)

Explanation:

The key realization is that our denominator fits the difference of squares pattern a^2-b^2, which factors as (a+b)(a-b).

We can rewrite x^2-25 as (x+5)(x-5), which allows us to rewrite our original expression as

(x+5)/((x+5)(x-5))

The x+5 terms on the top and bottom cancel, and we're left with

cancel(x+5)/(cancel(x+5)(x-5))

1/(x-5)

Hope this helps!

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