What is 5/(x-4)< 1/(x+4) ?

The solution to 5/(x-4)< 1/(x+4) is x<-6\lor-4<x<4

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5/(x-4)< 1/(x+4)

\frac{5}{x - 4} < \frac{1}{x + 4}

x < - 6 or - 4 < x < 4

Interval Notation

(- \infty, - 6) \cup (- 4, 4)

Solution steps

\frac{5}{x - 4} < \frac{1}{x + 4}

Rewrite in standard form

\frac{4 x + 24}{( x - 4 ) ( x + 4 )} < 0

Factor

\frac{4 x + 24}{( x - 4 ) ( x + 4 )} : \frac{4 ( x + 6 )}{( x - 4 ) ( x + 4 )}

\frac{4 ( x + 6 )}{( x - 4 ) ( x + 4 )} < 0

Divide both sides by

4

\frac{\frac{4 ( x + 6 )}{( x - 4 ) ( x + 4 )}}{4} < \frac{0}{4}

Simplify

\frac{x + 6}{( x - 4 ) ( x + 4 )} < 0

Identify the intervals

x < - 6 or - 4 < x < 4

\frac{w + 3}{4} = \frac{w - 2}{2}

(8 x + 7) (x + 1) = 9

6 x^{2} - 17 x + 13 = 20 x^{2} - 32

∣ 1 - 4 x ∣ - 11 < - 8

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