Question

How do you add `(a-1)/(a+1 )+ (a+1)/(a-1)`?

Answer 1

Convert the denominators to a common value and simplify to get
`color(white)("XXX")(2(a^2+1))/(a^2-1)`

Explanation:

`color(red)((a-1)/(a+1)) + color(blue)((a+1)/(a-1))`

`color(white)("XXX")=color(red)((a-1)/(a+1)) * (a-1)/(a-1) + (color(blue)(a+1)/(a-1)) * (a+1)/(a+1)`

`color(white)("XXX")=(color(green)((a-1)^2)+color(brown)((a+1)^2))/((a-1)(a+1)`

`color(white)("XXX")=(color(green)(a^2-2a+1)+color(brown)(a^2+2a+1))/((a-1)(a+1))`

`color(white)("XXX")=(2(a^2+1))/(a^2-1)`