Which is the solution of inequality ( x^2 - 1 ) / ( x^2 - 4) > -1

We'll add +1 both
sides E(x)>0.

( x^2 - 1 ) / ( x^2 - 4)
+1>0

We'll multiply 1 by the denominator ( x^2 -
4)

(x^2 - 1 + x^2 -
4)/(x^2-4)>0

(2*x^2-5)/(x^2-4)>0

The
numerator: f1(x)=2*x^2-5

The denominator
f2(x)=x^2-4

We'll discuss the sign of the
numerator.

For this reason, we'll calculate the solutions
of the equation f1(x)=0

2*x^2-5=0 => 2*x^2=5
=> x^2=5/2

x1= sqrt (5/2) and x2=-sqrt
(5/2)

For f1(x), with a=2>0, between it's
roots,we'll have the opposed sign to "a" sign, so the values of f1(x) are negative and
outside the roots, the values are positive.

f1(x)>0
for x belongs to (-inf,-sqrt(5/2))U(sqrt
(5/2),inf)

f2(x)<0 for x belongs to
(-sqrt(5/2),sqrt(5/2))

We'll discuss the sign of the
denominator f2(x)=x^2-4

f2(x)=
(x-2)(x+2)

(x-2)(x+2)=0

x1=2
and x2=-2

For f2(x), with a=1>0, between it's
roots,we'll have the opposed sign to "a" sign, so the values of f2(x) are negative and
outside the roots, the values are positive.

f2(x)>0
for x belongs to (-inf,-2)U(2,inf)

f2(x)<0 for x
belongs to (-2,2)

The intervals where
E(x)>0 are:

(-inf,-2) U
(-sqrt(5/2),sqrt(5/2)) U (2,inf)