Question

subtract the rational expressions and write the answer in simplest form.
$\frac{3x + 1}{2x^{2}}-\frac{2x - 1}{8x}$
$\frac{1}{8}$
$\frac{x + 2}{2x}$
$\frac{-2x^{2}+13x + 4}{8x^{2}}$
$\frac{-2x^{2}+4x + 1}{2x^{2}}$

Explanation:

Step1: Find common denominator

The common denominator of $2x^{2}$ and $8x$ is $8x^{2}$.

Step2: Rewrite fractions with common - denominator

$\frac{3x + 1}{2x^{2}}\times\frac{4}{4}=\frac{4(3x + 1)}{8x^{2}}=\frac{12x+4}{8x^{2}}$ and $\frac{2x - 1}{8x}\times\frac{x}{x}=\frac{x(2x - 1)}{8x^{2}}=\frac{2x^{2}-x}{8x^{2}}$.

Step3: Subtract the fractions

$\frac{12x + 4-(2x^{2}-x)}{8x^{2}}=\frac{12x + 4-2x^{2}+x}{8x^{2}}=\frac{-2x^{2}+13x + 4}{8x^{2}}$.

Answer:

$\frac{-2x^{2}+13x + 4}{8x^{2}}$