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

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

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

- 3 < x \leq - 1 or x > 1

Interval Notation

(- 3, - 1] \cup (1, \infty)

Solution steps

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

Rewrite in standard form

\frac{12 x + 12}{( - x + 1 ) ( x + 3 )} \leq 0

Factor

\frac{12 x + 12}{( - x + 1 ) ( x + 3 )} : \frac{12 ( x + 1 )}{( - x + 1 ) ( x + 3 )}

\frac{12 ( x + 1 )}{( - x + 1 ) ( x + 3 )} \leq 0

Divide both sides by

12

\frac{\frac{12 ( x + 1 )}{( - x + 1 ) ( x + 3 )}}{12} \leq \frac{0}{12}

Simplify

\frac{x + 1}{( - x + 1 ) ( x + 3 )} \leq 0

Identify the intervals

- 3 < x \leq - 1 or x > 1

(2 + 5 i) (5 - 3 i)

(\frac{2}{3})^{10}

x^{2} - 8 x - 33

16 u v^{2} y^{6} + 28 u^{4} v^{9}

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