What is (2x^2-2x-4)/(x^2-4)>0 ?

The solution to (2x^2-2x-4)/(x^2-4)>0 is x -1

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

\frac{2 x ^{2} - 2 x - 4}{x ^{2} - 4} > 0

x < - 2 or x > - 1

Interval Notation

(- \infty, - 2) \cup (- 1, \infty)

Solution steps

\frac{2 x ^{2} - 2 x - 4}{x ^{2} - 4} > 0

Factor

\frac{2 x ^{2} - 2 x - 4}{x ^{2} - 4} : \frac{2 ( x + 1 ) ( x - 2 )}{( x + 2 ) ( x - 2 )}

\frac{2 ( x + 1 ) ( x - 2 )}{( x + 2 ) ( x - 2 )} > 0

Divide both sides by

2

\frac{\frac{2 ( x + 1 ) ( x - 2 )}{( x + 2 ) ( x - 2 )}}{2} > \frac{0}{2}

Simplify

\frac{x + 1}{x + 2} > 0

Identify the intervals

x < - 2 or x > - 1

90 x^{2} - 200 y^{2}

- 3 x^{2} + 5 x + 3 = 0

2 y^{2} - 11 y + 5

x^{2} + 5 x - 14 \geq 0

x (x - 4) \leq 5

What is (2x^2-2x-4)/(x^2-4)>0 ?
The solution to (2x^2-2x-4)/(x^2-4)>0 is x<-2\lor x>-1