What is x/((x+4))-1/((x+1))<= 0 ?

The solution to x/((x+4))-1/((x+1))<= 0 is -4<x<=-2\lor-1<x<= 2

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x/((x+4))-1/((x+1))<= 0

\frac{x}{( x + 4 )} - \frac{1}{( x + 1 )} \leq 0

- 4 < x \leq - 2 or - 1 < x \leq 2

Interval Notation

(- 4, - 2] \cup (- 1, 2]

Solution steps

\frac{x}{x + 4} - \frac{1}{x + 1} \leq 0

Rewrite in standard form

\frac{x ^{2} - 4}{( x + 4 ) ( x + 1 )} \leq 0

Factor

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

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

Identify the intervals

- 4 < x \leq - 2 or - 1 < x \leq 2

2 + \frac{3}{x} + 1 - \frac{2}{x} > 0

\frac{( x + 3 )}{( x - 1 )} > x

\frac{x ^{2}}{x - 1} \geq 0

\frac{( x - 9 ) ( x - 15 )}{( x - 12 )} > 0

m^{2} + 8 > 0

What is x/((x+4))-1/((x+1))<= 0 ?
The solution to x/((x+4))-1/((x+1))<= 0 is -4<x<=-2\lor-1<x<= 2