What is 6/(x-3)< 3/(x+1) ?

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

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6/(x-3)< 3/(x+1)

\frac{6}{x - 3} < \frac{3}{x + 1}

x < - 5 or - 1 < x < 3

Interval Notation

(- \infty, - 5) \cup (- 1, 3)

Solution steps

\frac{6}{x - 3} < \frac{3}{x + 1}

Rewrite in standard form

\frac{3 x + 15}{( x - 3 ) ( x + 1 )} < 0

Factor

\frac{3 x + 15}{( x - 3 ) ( x + 1 )} : \frac{3 ( x + 5 )}{( x - 3 ) ( x + 1 )}

\frac{3 ( x + 5 )}{( x - 3 ) ( x + 1 )} < 0

Divide both sides by

3

\frac{\frac{3 ( x + 5 )}{( x - 3 ) ( x + 1 )}}{3} < \frac{0}{3}

Simplify

\frac{x + 5}{( x - 3 ) ( x + 1 )} < 0

Identify the intervals

x < - 5 or - 1 < x < 3

(x + 7)^{2} (x + 2) (x - 1) > 0

4^{5} \cdot 4^{3}

\frac{2}{i 2}

3 x + 2 = - 2 x - 1

2 (x - 5) < 8