What is 1/3 < 1/(x-2)-1/(x+2) ?

The solution to 1/3 < 1/(x-2)-1/(x+2) is -4<x<-2\lor 2<x<4

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1/3 < 1/(x-2)-1/(x+2)

\frac{1}{3} < \frac{1}{x - 2} - \frac{1}{x + 2}

- 4 < x < - 2 or 2 < x < 4

Interval Notation

(- 4, - 2) \cup (2, 4)

Solution steps

\frac{1}{3} < \frac{1}{x - 2} - \frac{1}{x + 2}

Switch sides

\frac{1}{x - 2} - \frac{1}{x + 2} > \frac{1}{3}

Rewrite in standard form

\frac{- x ^{2} + 16}{( x - 2 ) ( x + 2 )} > 0

Factor

\frac{- x ^{2} + 16}{( x - 2 ) ( x + 2 )} : \frac{- ( x + 4 ) ( x - 4 )}{( x - 2 ) ( x + 2 )}

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

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 4 ) ( x - 4 ) ) ( - 1 )}{( x - 2 ) ( x + 2 )} < 0 \cdot (- 1)

Simplify

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

Identify the intervals

- 4 < x < - 2 or 2 < x < 4

9 u^{2} - 30 uv + 25 v^{2}

\frac{3}{2 5}

6 z^{2} - z = 0

- 3 \cdot 7

1. 1^{6}

What is 1/3 < 1/(x-2)-1/(x+2) ?
The solution to 1/3 < 1/(x-2)-1/(x+2) is -4<x<-2\lor 2<x<4