Answer:
[tex]\frac{2}{a-b}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{a+b}[/tex] + [tex]\frac{1}{a-b}[/tex] + [tex]\frac{2b}{a^2-b^2}[/tex] ← a² - b² is a difference of squares
= [tex]\frac{1}{a+b}[/tex] + [tex]\frac{1}{a-b}[/tex] = [tex]\frac{2b}{(a-b)(a+b)}[/tex] ← LCD is (a - b)(a+b)
= [tex]\frac{a-b+a+b+2b}{(a-b)(a+b)}[/tex]
= [tex]\frac{2a+2b}{(a-b)(a+b)}[/tex]
= [tex]\frac{2(a+b)}{(a-b)(a+b)}[/tex] ← cancel common factor (a + b) on numerator/ denominator
= [tex]\frac{2}{a-b}[/tex]
