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

The solution to (x+2)/(x-4)<(x+2)/(x+3) is x<-3\lor-2<x<4

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(x+2)/(x-4)<(x+2)/(x+3)

\frac{x + 2}{x - 4} < \frac{x + 2}{x + 3}

x < - 3 or - 2 < x < 4

Solution steps

\frac{x + 2}{x - 4} < \frac{x + 2}{x + 3}

Rewrite in standard form

\frac{7 x + 14}{( x - 4 ) ( x + 3 )} < 0

Factor

\frac{7 x + 14}{( x - 4 ) ( x + 3 )} : \frac{7 ( x + 2 )}{( x - 4 ) ( x + 3 )}

\frac{7 ( x + 2 )}{( x - 4 ) ( x + 3 )} < 0

Divide both sides by

7

\frac{\frac{7 ( x + 2 )}{( x - 4 ) ( x + 3 )}}{7} < \frac{0}{7}

Simplify

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

Identify the intervals

x < - 3 or - 2 < x < 4

3 m p + 8 + 2 p + 12 m

∣ 2 x - 4 ∣ = ∣ 3 x - 9 ∣

3 k^{2} + 5 k + 2

a^{2} + 3 a - 28

\frac{7}{4} - (\frac{5}{3} + \frac{2}{3} \cdot \frac{1}{5}) + 2

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