What is ((x+1))/((x+2))-x/(x+3)<= 7/((x^2+5x+6)) ?

The solution to ((x+1))/((x+2))-x/(x+3)<= 7/((x^2+5x+6)) is x<-3\lor-2<x<= 2

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((x+1))/((x+2))-x/(x+3)<= 7/((x^2+5x+6))

\frac{( x + 1 )}{( x + 2 )} - \frac{x}{x + 3} \leq \frac{7}{( x ^{2} + 5 x + 6 )}

x < - 3 or - 2 < x \leq 2

Interval Notation

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

Solution steps

\frac{x + 1}{x + 2} - \frac{x}{x + 3} \leq \frac{7}{x ^{2} + 5 x + 6}

Rewrite in standard form

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

Factor

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

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

x < - 3 or - 2 < x \leq 2

2 x^{2} + 4 x + 9 = 0

- 142 = - 40 - 6 x

- 6 m - 14 < 15

x - 7 = - 4

(\frac{1}{5} k)^{2}

What is ((x+1))/((x+2))-x/(x+3)<= 7/((x^2+5x+6)) ?
The solution to ((x+1))/((x+2))-x/(x+3)<= 7/((x^2+5x+6)) is x<-3\lor-2<x<= 2