What is (x+1)/2 <(x+2)/(1-x) ?

The solution to (x+1)/2 <(x+2)/(1-x) is x<1

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(x+1)/2 <(x+2)/(1-x)

\frac{x + 1}{2} < \frac{x + 2}{1 - x}

x < 1

Solution steps

\frac{x + 1}{2} < \frac{x + 2}{1 - x}

Rewrite in standard form

\frac{- x ^{2} - 2 x - 3}{- x + 1} < 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x < 1

0 = x^{2} + 20 x - 4

7 + x \leq 2 (x + 3) + 2

\frac{4 x - 3}{2} - \frac{3 x - 3}{3} < 3

3 x^{2} + 2 x - 26 = 0

- 41 a - 4 = 47 a - 3