What is ((x-1))/((x+2))>= ((x-3))/((x+4)) ?

The solution to ((x-1))/((x+2))>= ((x-3))/((x+4)) is -4 =-1/2

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((x-1))/((x+2))>= ((x-3))/((x+4))

\frac{( x - 1 )}{( x + 2 )} \geq \frac{( x - 3 )}{( x + 4 )}

- 4 < x < - 2 or x \geq - \frac{1}{2}

Interval Notation

(- 4, - 2) \cup [- \frac{1}{2}, \infty)

Decimal Notation

- 4 < x < - 2 or x \geq - 0.5

Solution steps

\frac{x - 1}{x + 2} \geq \frac{x - 3}{x + 4}

Rewrite in standard form

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

Factor

\frac{4 x + 2}{( x + 2 ) ( x + 4 )} : \frac{2 ( 2 x + 1 )}{( x + 2 ) ( x + 4 )}

\frac{2 ( 2 x + 1 )}{( x + 2 ) ( x + 4 )} \geq 0

Divide both sides by

2

\frac{\frac{2 ( 2 x + 1 )}{( x + 2 ) ( x + 4 )}}{2} \geq \frac{0}{2}

Simplify

\frac{2 x + 1}{( x + 2 ) ( x + 4 )} \geq 0

Identify the intervals

- 4 < x < - 2 or x \geq - \frac{1}{2}

x^{3} - 6 x^{2} + 11 x - 6 \leq 0

\frac{1}{m} \leq - 1

(x + 2) (2 x - 1) > 0

x^{2} + 2 x + 3 < 0

(x + 5)^{5} \cdot (x - 2)^{2} \cdot (x - 5)^{5} < 0

What is ((x-1))/((x+2))>= ((x-3))/((x+4)) ?
The solution to ((x-1))/((x+2))>= ((x-3))/((x+4)) is -4<x<-2\lor x>=-1/2