What is 1+6/(x+1)<= 6/x ?

The solution to 1+6/(x+1)<= 6/x is -3<= x<-1\lor 0<x<= 2

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1+6/(x+1)<= 6/x

1 + \frac{6}{x + 1} \leq \frac{6}{x}

- 3 \leq x < - 1 or 0 < x \leq 2

Interval Notation

[- 3, - 1) \cup (0, 2]

Solution steps

1 + \frac{6}{x + 1} \leq \frac{6}{x}

Rewrite in standard form

\frac{x ^{2} + x - 6}{x ( x + 1 )} \leq 0

Factor

\frac{x ^{2} + x - 6}{x ( x + 1 )} : \frac{( x - 2 ) ( x + 3 )}{x ( x + 1 )}

\frac{( x - 2 ) ( x + 3 )}{x ( x + 1 )} \leq 0

Identify the intervals

- 3 \leq x < - 1 or 0 < x \leq 2

a^{10} - 28 a^{5} + 27

x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1

w^{2} - 10 w + 25 = 0

3220

\frac{1}{11.73913} - \frac{1}{12}

What is 1+6/(x+1)<= 6/x ?
The solution to 1+6/(x+1)<= 6/x is -3<= x<-1\lor 0<x<= 2