What is 4/((x-5))-2/((x-5))>((3x+3))/((x^2-25)) ?

The solution to 4/((x-5))-2/((x-5))>((3x+3))/((x^2-25)) is x<-5\lor 5<x<7

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4/((x-5))-2/((x-5))>((3x+3))/((x^2-25))

\frac{4}{( x - 5 )} - \frac{2}{( x - 5 )} > \frac{( 3 x + 3 )}{( x ^{2} - 25 )}

x < - 5 or 5 < x < 7

Interval Notation

(- \infty, - 5) \cup (5, 7)

Solution steps

\frac{4}{x - 5} - \frac{2}{x - 5} > \frac{3 x + 3}{x ^{2} - 25}

Rewrite in standard form

\frac{- x + 7}{( x - 5 ) ( x + 5 )} > 0

Identify the intervals

x < - 5 or 5 < x < 7

- 4 - 3 x^{2} > 0

6 x^{3} + 7 x^{2} - 20 x > 0

\frac{( 2 x ^{2} )}{( x - 5 )} > - 5

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

6 x^{3} - x^{2} < 8 - 48 x

What is 4/((x-5))-2/((x-5))>((3x+3))/((x^2-25)) ?
The solution to 4/((x-5))-2/((x-5))>((3x+3))/((x^2-25)) is x<-5\lor 5<x<7