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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.

User JayTee
by
8.1k points

1 Answer

3 votes

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.

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.

User CrouZ
by
7.9k points
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