1/a+b + 1/a-b +2b/a^2-b^2 simplify

Question

asked Sep 8, 2022 33.2k views

1 Answer

Hroncok · Answer 1 · 2022-09-15T11:53:46+0000

Answer:

(2)/(a-b)

Explanation:

Given

(1)/(a+b) +
(1)/(a-b) +
(2b)/(a^2-b^2) ← a² - b² is a difference of squares

=
(1)/(a+b) +
(1)/(a-b) =
(2b)/((a-b)(a+b)) ← LCD is (a - b)(a+b)

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

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

=
(2(a+b))/((a-b)(a+b)) ← cancel common factor (a + b) on numerator/ denominator

=
(2)/(a-b)