What is 4/((x-1))< 3/((x+5)) ?

The solution to 4/((x-1))< 3/((x+5)) is x<-23\lor-5<x<1

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4/((x-1))< 3/((x+5))

\frac{4}{( x - 1 )} < \frac{3}{( x + 5 )}

x < - 23 or - 5 < x < 1

Interval Notation

(- \infty, - 23) \cup (- 5, 1)

Solution steps

\frac{4}{x - 1} < \frac{3}{x + 5}

Rewrite in standard form

\frac{x + 23}{( x - 1 ) ( x + 5 )} < 0

Identify the intervals

x < - 23 or - 5 < x < 1

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

\frac{( ( x + 2 ) ( x ^{2} - 2 x + 1 ) )}{( - 4 + 3 x - x ^{2} )} \geq 0

\frac{( 6 )}{( x ^{2} - 4 x + 4 )} > 0

\frac{1}{2 ( 4 x + 14 )} < 3 x - 6

\frac{( 3 p + 5 )}{( 5 p - 9 )} > \frac{2}{7}

What is 4/((x-1))< 3/((x+5)) ?
The solution to 4/((x-1))< 3/((x+5)) is x<-23\lor-5<x<1