What is (x^2)/(x+2)<(12-x)/(x+2) ?

The solution to (x^2)/(x+2)<(12-x)/(x+2) is x<-4\lor-2<x<3

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(x^2)/(x+2)<(12-x)/(x+2)

\frac{x ^{2}}{x + 2} < \frac{12 - x}{x + 2}

x < - 4 or - 2 < x < 3

Solution steps

\frac{x ^{2}}{x + 2} < \frac{12 - x}{x + 2}

Rewrite in standard form

\frac{x ^{2} - 12 + x}{x + 2} < 0

Factor

\frac{x ^{2} - 12 + x}{x + 2} : \frac{( x - 3 ) ( x + 4 )}{x + 2}

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

Identify the intervals

x < - 4 or - 2 < x < 3

6 x^{2} + 90 x + 324

(\frac{x}{40}) + 25% x = 500

3 a + 5 a^{2} = 2

4 x - 5 + 4 x - 5 = 90

\frac{1000 0 ^{2} \cdot 1.5 \cdot 1 0 ^{- 12}}{3.5}

What is (x^2)/(x+2)<(12-x)/(x+2) ?
The solution to (x^2)/(x+2)<(12-x)/(x+2) is x<-4\lor-2<x<3