Solve the inequality f(x)>-1. f(x)=(x-1)(x+1)/(x+2)(x-2)

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We have to solve f(x) > -1 for f(x)=(x-1)(x+1)/(x+2)(x-2)

f(x) > -1

=> (x-1)(x+1)/(x+2)(x-2) > -1

=> (x-1)(x+1) > -1*(x+2)(x-2)

=> x^2 - 1 > -1* (x^2 - 4)

=> x^2 - 1 > -x^2 + 4

=> 2x^2 > 5

=> x^2 > 5/2

=> x > sqrt 5/2...

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We have to solve f(x) > -1 for f(x)=(x-1)(x+1)/(x+2)(x-2)

f(x) > -1

=> (x-1)(x+1)/(x+2)(x-2) > -1

=> (x-1)(x+1) > -1*(x+2)(x-2)

=> x^2 - 1 > -1* (x^2 - 4)

=> x^2 - 1 > -x^2 + 4

=> 2x^2 > 5

=> x^2 > 5/2

=> x > sqrt 5/2 or x < -sqrt 5/2

Therefore x lies in (-inf , -(sqrt 5)/2) and ((sqrt 5)/2 , + inf)

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