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

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

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

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

x < - 5 or - 1 \leq x < 1

Interval Notation

(- \infty, - 5) \cup [- 1, 1)

Solution steps

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

Rewrite in standard form

\frac{12 x + 12}{( x - 1 ) ( x + 5 )} \leq 0

Factor

\frac{12 x + 12}{( x - 1 ) ( x + 5 )} : \frac{12 ( x + 1 )}{( x - 1 ) ( x + 5 )}

\frac{12 ( x + 1 )}{( x - 1 ) ( x + 5 )} \leq 0

Divide both sides by

12

\frac{\frac{12 ( x + 1 )}{( x - 1 ) ( x + 5 )}}{12} \leq \frac{0}{12}

Simplify

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

Identify the intervals

x < - 5 or - 1 \leq x < 1

\frac{20 x ^{7} y ^{10}}{y ^{2}}

x^{3} + 6 x^{2} + 5 x - 12

5 \cdot 5

x (2 x + 3) \geq 5

2 x^{2} + 16 x - 10 = 0

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