What is ((x-4))/((x+2))>= ((x-5))/((x+4)) ?

The solution to ((x-4))/((x+2))>= ((x-5))/((x+4)) is -4 = 2

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((x-4))/((x+2))>= ((x-5))/((x+4))

\frac{( x - 4 )}{( x + 2 )} \geq \frac{( x - 5 )}{( x + 4 )}

- 4 < x < - 2 or x \geq 2

Interval Notation

(- 4, - 2) \cup [2, \infty)

Solution steps

\frac{x - 4}{x + 2} \geq \frac{x - 5}{x + 4}

Rewrite in standard form

\frac{3 x - 6}{( x + 2 ) ( x + 4 )} \geq 0

Factor

\frac{3 x - 6}{( x + 2 ) ( x + 4 )} : \frac{3 ( x - 2 )}{( x + 2 ) ( x + 4 )}

\frac{3 ( x - 2 )}{( x + 2 ) ( x + 4 )} \geq 0

Divide both sides by

3

\frac{\frac{3 ( x - 2 )}{( x + 2 ) ( x + 4 )}}{3} \geq \frac{0}{3}

Simplify

\frac{x - 2}{( x + 2 ) ( x + 4 )} \geq 0

Identify the intervals

- 4 < x < - 2 or x \geq 2

x^{3} + 9 x^{2} \leq - 26 x - 24

x, f < - 8

x^{2} > 4 (8 - x)

(x - 1) (\frac{x}{2}) < 0

\frac{( x ^{2} - 5 x + 6 )}{( x - 1 )} > 0

What is ((x-4))/((x+2))>= ((x-5))/((x+4)) ?
The solution to ((x-4))/((x+2))>= ((x-5))/((x+4)) is -4<x<-2\lor x>= 2