What is 1/(3(x-2))+1/((x+1)(2-x))>0 ?

The solution to 1/(3(x-2))+1/((x+1)(2-x))>0 is x>-1

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1/(3(x-2))+1/((x+1)(2-x))>0

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

x > - 1

Interval Notation

(- 1, \infty)

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

- \frac{1}{x + 1} < 0

Identify the intervals

x > - 1

- lo g_{10} (0.1)

(2 + 3 i) (8 - 7 i)

2 + 8

\frac{12}{c ^{- 8} d ^{2}}

4 x^{2} - 32 x + 39 = 0

What is 1/(3(x-2))+1/((x+1)(2-x))>0 ?
The solution to 1/(3(x-2))+1/((x+1)(2-x))>0 is x>-1