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

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

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

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

x < - 2 or x > - 2

Interval Notation

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

Solution steps

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

Rewrite in standard form

\frac{2 x - 4}{( x + 2 ) ^{2} ( x - 2 )} > 0

Factor

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

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

x < - 2 or x > - 2

2 (x - 3)^{2} = 8

\frac{- 2}{3} = \frac{x}{9}

- 3 x^{2} y^{3} (- 14 x^{3} y^{5})

y^{2} + 9 y + 8 = 0

(- 2 + 3 i) (- 2 - 3 i)

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