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

Popular >

1/x < x/(x+2)

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

x < - 2 or - 1 < x < 0 or x > 2

Interval Notation

(- \infty, - 2) \cup (- 1, 0) \cup (2, \infty)

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x < - 2 or - 1 < x < 0 or x > 2

(q^{9})^{2}

0.000189707 x^{2} + 0.982889 x + 0.0852592 = 0

w^{2} + 2 w - 24

1 + a^{10} - 2 a^{5}

6 x - \frac{2 x + 3}{5} = \frac{x - 5}{4} - x