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

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

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

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

x < - 2 or 2 < x \leq 4

Interval Notation

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

Solution steps

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

Rewrite in standard form

\frac{2 x - 8}{( x + 2 ) ( x - 2 )} \leq 0

Factor

\frac{2 x - 8}{( x + 2 ) ( x - 2 )} : \frac{2 ( x - 4 )}{( x + 2 ) ( x - 2 )}

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

x < - 2 or 2 < x \leq 4

3 x^{2} + 6 x = 0

lo g_{10} (36)

\frac{1}{- 4 + 2}

4 x = x^{2}

∣ k - 10 ∣ + 10 = 2

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