$\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } 0$ A) $x 0$ B) $x - 2$ C) $x

Name: $\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } > 0$ A) $x > 0$ B) $x > - 2$ C) $x < - \frac { 1 } { 2 }$ D) $x < - 2$
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Question

$\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } > 0$ A) $x > 0$ B) $x > - 2$ C) $x < - \frac { 1 } { 2 }$ D) $x < - 2$

Quizplus · Accepted Answer

The inequality $\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } > 0$ simplifies to $\frac { 3(x + 2) } { 5(x ^ { 2 } + 1) } > 0$. Since $x^2 + 1$ is always positive, the sign of the expression depends on $3(x + 2)$. This is positive when $x + 2 > 0$, or $x > -2$.

3x+65x2+5>0\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } > 05x2+53x+6​>0

$\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } > 0$