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

The solution to (x-1)/(x+3)>(x-4)/(x+2) is -5 -2

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

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

- 5 < x < - 3 or x > - 2

Interval Notation

(- 5, - 3) \cup (- 2, \infty)

Solution steps

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

Rewrite in standard form

\frac{2 x + 10}{( x + 3 ) ( x + 2 )} > 0

Factor

\frac{2 x + 10}{( x + 3 ) ( x + 2 )} : \frac{2 ( x + 5 )}{( x + 3 ) ( x + 2 )}

\frac{2 ( x + 5 )}{( x + 3 ) ( x + 2 )} > 0

Divide both sides by

2

\frac{\frac{2 ( x + 5 )}{( x + 3 ) ( x + 2 )}}{2} > \frac{0}{2}

Simplify

\frac{x + 5}{( x + 3 ) ( x + 2 )} > 0

Identify the intervals

- 5 < x < - 3 or x > - 2

4 - \frac{8}{3}

2 y^{2} = 18

100 + 100 r t

2 x = 1

What is (x-1)/(x+3)>(x-4)/(x+2) ?
The solution to (x-1)/(x+3)>(x-4)/(x+2) is -5<x<-3\lor x>-2