What is (x-1)/(x-5)>= (x+5)/(x+9) ?

The solution to (x-1)/(x-5)>= (x+5)/(x+9) is -9 5

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(x-1)/(x-5)>= (x+5)/(x+9)

\frac{x - 1}{x - 5} \geq \frac{x + 5}{x + 9}

- 9 < x \leq - 2 or x > 5

Interval Notation

(- 9, - 2] \cup (5, \infty)

Solution steps

\frac{x - 1}{x - 5} \geq \frac{x + 5}{x + 9}

Rewrite in standard form

\frac{8 x + 16}{( x - 5 ) ( x + 9 )} \geq 0

Factor

\frac{8 x + 16}{( x - 5 ) ( x + 9 )} : \frac{8 ( x + 2 )}{( x - 5 ) ( x + 9 )}

\frac{8 ( x + 2 )}{( x - 5 ) ( x + 9 )} \geq 0

Divide both sides by

8

\frac{\frac{8 ( x + 2 )}{( x - 5 ) ( x + 9 )}}{8} \geq \frac{0}{8}

Simplify

\frac{x + 2}{( x - 5 ) ( x + 9 )} \geq 0

Identify the intervals

- 9 < x \leq - 2 or x > 5

\frac{1}{\frac{4}{2}}

5 < \frac{x - 6}{2} < 16

8 x - 11 (x - 2) = - 8

\frac{y ^{- 1} + x ^{- 1}}{( x y ) ^{- 1}}

\frac{w - 5.4}{- 1} = - 2.8

What is (x-1)/(x-5)>= (x+5)/(x+9) ?
The solution to (x-1)/(x-5)>= (x+5)/(x+9) is -9<x<=-2\lor x>5