What is (x-1)/(x+1)<= (x+3)/(x-5) ?

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(x-1)/(x+1)<= (x+3)/(x-5)

\frac{x - 1}{x + 1} \leq \frac{x + 3}{x - 5}

- 1 < x \leq \frac{1}{5} or x > 5

Interval Notation

(- 1, \frac{1}{5}] \cup (5, \infty)

Decimal Notation

- 1 < x \leq 0.2 or x > 5

Solution steps

\frac{x - 1}{x + 1} \leq \frac{x + 3}{x - 5}

Rewrite in standard form

\frac{- 10 x + 2}{( x + 1 ) ( x - 5 )} \leq 0

Factor

\frac{- 10 x + 2}{( x + 1 ) ( x - 5 )} : \frac{- 2 ( 5 x - 1 )}{( x + 1 ) ( x - 5 )}

\frac{- 2 ( 5 x - 1 )}{( x + 1 ) ( x - 5 )} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 2 ( 5 x - 1 ) ) ( - 1 )}{( x + 1 ) ( x - 5 )} \geq 0 \cdot (- 1)

Simplify

\frac{2 ( 5 x - 1 )}{( x + 1 ) ( x - 5 )} \geq 0

Divide both sides by

2

\frac{\frac{2 ( 5 x - 1 )}{( x + 1 ) ( x - 5 )}}{2} \geq \frac{0}{2}

Simplify

\frac{5 x - 1}{( x + 1 ) ( x - 5 )} \geq 0

Identify the intervals

- 1 < x \leq \frac{1}{5} or x > 5

x^{2} - 5 x = 14

(\frac{3 x ^{2} y ^{5} z ^{- 2}}{5 x z ^{5}})^{- 3}

5 x^{2} + 6 x = - 5

y, 2 x - y + 5^{x - 1} = 7 \cdot 5

16 - 4

What is (x-1)/(x+1)<= (x+3)/(x-5) ?
The solution to (x-1)/(x+1)<= (x+3)/(x-5) is -1<x<= 1/5 \lor x>5