What is ((14x))/((x+1))-((9x-30))/((x-4))<0 ?

The solution to ((14x))/((x+1))-((9x-30))/((x-4))<0 is -1<x<1\lor 4<x<6

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((14x))/((x+1))-((9x-30))/((x-4))<0

\frac{( 14 x )}{( x + 1 )} - \frac{( 9 x - 30 )}{( x - 4 )} < 0

- 1 < x < 1 or 4 < x < 6

Interval Notation

(- 1, 1) \cup (4, 6)

Solution steps

\frac{14 x}{x + 1} - \frac{9 x - 30}{x - 4} < 0

Rewrite in standard form

\frac{5 x ^{2} - 35 x + 30}{( x + 1 ) ( x - 4 )} < 0

Factor

\frac{5 x ^{2} - 35 x + 30}{( x + 1 ) ( x - 4 )} : \frac{5 ( x - 1 ) ( x - 6 )}{( x + 1 ) ( x - 4 )}

\frac{5 ( x - 1 ) ( x - 6 )}{( x + 1 ) ( x - 4 )} < 0

Divide both sides by

5

\frac{\frac{5 ( x - 1 ) ( x - 6 )}{( x + 1 ) ( x - 4 )}}{5} < \frac{0}{5}

Simplify

\frac{( x - 1 ) ( x - 6 )}{( x + 1 ) ( x - 4 )} < 0

Identify the intervals

- 1 < x < 1 or 4 < x < 6

\frac{1}{( 3 x - 2 )} \leq \frac{1}{( 3 x + 4 )}

n^{5} - n^{3} < 0

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

\frac{3 \cdot ( 1 - x )}{2 + 2 x - 1} > \frac{3 x - 1}{2}

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

What is ((14x))/((x+1))-((9x-30))/((x-4))<0 ?
The solution to ((14x))/((x+1))-((9x-30))/((x-4))<0 is -1<x<1\lor 4<x<6