Question

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

Answer 1

Answer:

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.

Step-by-step explanation:

The given expression is

$(\frac{5}{a+1}-\frac{3}{a-1}+\frac{6}{a^2-1})\times \frac{a+1}{2}$

$(\frac{5(a-1)-3(a+1)+6}{a^2-1})\times \frac{a+1}{2}$

$(\frac{5a-5-3a-3+6}{a^2-1})\times \frac{a+1}{2}$

$(\frac{2a-2}{a^2-1})\times \frac{a+1}{2}$

$(\frac{2(a-1)}{(a-1)(a+1)})\times \frac{a+1}{2}$

$\frac{2(a-1)(a+1)}{2(a-1)(a+1)}$

Cancel out the common factors.

$\frac{2(a-1)(a+1)}{2(a-1)(a+1)}=1$

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.