What is ((x+2)(2x-3))/((x-3)(x+1))>6 ?

The solution to ((x+2)(2x-3))/((x-3)(x+1))>6 is -1<x<-3/4 \lor 3<x<4

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((x+2)(2x-3))/((x-3)(x+1))>6

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

- 1 < x < - \frac{3}{4} or 3 < x < 4

Solution steps

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

Rewrite in standard form

\frac{- 4 x ^{2} + 13 x + 12}{( x - 3 ) ( x + 1 )} > 0

Factor

\frac{- 4 x ^{2} + 13 x + 12}{( x - 3 ) ( x + 1 )} : \frac{- ( 4 x + 3 ) ( x - 4 )}{( x - 3 ) ( x + 1 )}

\frac{- ( 4 x + 3 ) ( x - 4 )}{( x - 3 ) ( x + 1 )} > 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

- 1 < x < - \frac{3}{4} or 3 < x < 4

\frac{( 2 x ) ^{2}}{( 10 ) ^{3}} = 2 \cdot 1 0^{- 6}

25 \cdot 15

u^{2} + 2 u - 3

x^{2} + 16 x - 21 = - 5

∣ t ∣ = 2

What is ((x+2)(2x-3))/((x-3)(x+1))>6 ?
The solution to ((x+2)(2x-3))/((x-3)(x+1))>6 is -1<x<-3/4 \lor 3<x<4