What is (x-2)/(x-5)>= (x+5)/(x+9) ?

The solution to (x-2)/(x-5)>= (x+5)/(x+9) is -9 5

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(x-2)/(x-5)>= (x+5)/(x+9)

\frac{x - 2}{x - 5} \geq \frac{x + 5}{x + 9}

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

Interval Notation

(- 9, - 1] \cup (5, \infty)

Solution steps

\frac{x - 2}{x - 5} \geq \frac{x + 5}{x + 9}

Rewrite in standard form

\frac{7 x + 7}{( x - 5 ) ( x + 9 )} \geq 0

Factor

\frac{7 x + 7}{( x - 5 ) ( x + 9 )} : \frac{7 ( x + 1 )}{( x - 5 ) ( x + 9 )}

\frac{7 ( x + 1 )}{( x - 5 ) ( x + 9 )} \geq 0

Divide both sides by

7

\frac{\frac{7 ( x + 1 )}{( x - 5 ) ( x + 9 )}}{7} \geq \frac{0}{7}

Simplify

\frac{x + 1}{( x - 5 ) ( x + 9 )} \geq 0

Identify the intervals

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

- 5 x^{2} - 12 x + 9

81 x^{2} - 196 y^{2}

12 \cdot 14

\frac{π}{2} + 2 π

8 x^{3} - 27

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