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

\frac{a ^{2}}{( a ^{4} + 1 )} \geq \frac{1}{2}

x^{3} - 4 x^{2} + 2 < x^{3} - 2 x^{2} + 1

\frac{- 3}{- x + 7} > 0

\frac{1}{( x - 1 )} \leq 2

3 x^{3} \geq 12

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