Question

subtract the rational expressions and write the answer in simplest form
$\frac{3x}{9x}-\frac{4x - 1}{6x^{2}}$
$\frac{-x - 1}{3x}$
$\frac{-x + 1}{6x}$
$\frac{3x^{2}+4x + 1}{3x^{2}}$
$\frac{2x^{2}-4x + 1}{6x^{2}}$

Explanation:

Step1: Find common denominator

The denominators are $9x$ and $6x^{2}$. The least - common denominator (LCD) of $9x$ and $6x^{2}$ is $18x^{2}$.

Step2: Rewrite fractions with LCD

Rewrite $\frac{3x}{9x}$ as $\frac{3x\cdot2x}{9x\cdot2x}=\frac{6x^{2}}{18x^{2}}$, and $\frac{4x - 1}{6x^{2}}$ as $\frac{(4x - 1)\cdot3}{6x^{2}\cdot3}=\frac{12x-3}{18x^{2}}$.

Step3: Subtract the fractions

$\frac{6x^{2}}{18x^{2}}-\frac{12x - 3}{18x^{2}}=\frac{6x^{2}-(12x - 3)}{18x^{2}}=\frac{6x^{2}-12x + 3}{18x^{2}}$.

Step4: Simplify the fraction

Factor out a 3 from the numerator: $\frac{3(2x^{2}-4x + 1)}{18x^{2}}=\frac{2x^{2}-4x + 1}{6x^{2}}$.

Answer:

$\frac{2x^{2}-4x + 1}{6x^{2}}$