# How do you simplify (2)/(x^2+1)*(3)/(2x)?

Apr 27, 2018

$\frac{3}{{x}^{3} + x}$

#### Explanation:

When multiplying fractions just multiply the numerators to get your new numerator and multiply the denominators to get your new denominator.

Numerator:

$2 \cdot 3 = 6$

Denominator:

$\left({x}^{2} + 1\right) \cdot 2 x$

$\implies 2 x \left({x}^{2} + 1\right)$

Distribute

$2 x \cdot {x}^{2} + 2 x \cdot 1$

$\implies 2 {x}^{3} + 2 x$

Result fraction

$\frac{6}{2 {x}^{3} + 2 x}$

Factor a $2$ out of the denominator

$\frac{6}{2 \left(\frac{2}{2} {x}^{3} + \frac{2}{2} x\right)}$

$\frac{6}{2 \left({x}^{3} + x\right)}$

Simplify

$\frac{3}{{x}^{3} + x}$