Simplify this expression?

Question

(a / (a - 1)) - (3 /( a^2 - 1))

Answer 1

Given expression is (a / (a - 1)) - (3 /( a^2 - 1))

= (a / (a - 1)) - (3 /( a^2 - 1))

The LCM of a -1 and a^2 - 1 is a^2 - 1

= ( a (a + 1) - 3 (1) ) / a^2 - 1

= ( a^2 + a - 3 ) / a^2 - 1