Question

Prove that for all admissible values of a, the value of the expression

(5 / a+1 - 3 / a-1 + 6 / a^2 - 1)* (a + 1)/2

does not depend on the variable a.

Answer 1

The simplified value of given expression is 1, which is free from a, therefore the value of the expression does not depend on the variable a.

Explanation:

The given expression is

`((5)/(a+1)-(3)/(a-1)+(6)/(a^2-1))* (a+1)/(2)`

`((5(a-1)-3(a+1)+6)/(a^2-1))* (a+1)/(2)`

`((5a-5-3a-3+6)/(a^2-1))* (a+1)/(2)`

`((2a-2)/(a^2-1))* (a+1)/(2)`

`((2(a-1))/((a-1)(a+1)))* (a+1)/(2)`

`(2(a-1)(a+1))/(2(a-1)(a+1))`

Cancel out the common factors.

`(2(a-1)(a+1))/(2(a-1)(a+1))=1`

Since the simplified value of given expression is 1, which is free from a, therefore the value of the expression does not depend on the variable a.