Question

add the rational expressions and write the answer in simplest form $\frac{4x - 1}{6x^{2}}+\frac{3x}{9x}$
$\frac{7x - 1}{3x}$
$\frac{6x - 1}{6x}$
$\frac{3x^{2}+4x - 1}{3x^{2}}$
$\frac{2x^{2}+4x - 1}{6x^{2}}$

Explanation:

Step1: Find the common denominator

The denominators are $6x^{2}$ and $9x$. The least - common multiple of $6x^{2}$ and $9x$ is $18x^{2}$.

Step2: Rewrite the fractions with the common denominator

$\frac{4x - 1}{6x^{2}}\times\frac{3}{3}=\frac{3(4x - 1)}{18x^{2}}=\frac{12x-3}{18x^{2}}$; $\frac{3x}{9x}\times\frac{2x}{2x}=\frac{6x^{2}}{18x^{2}}$.

Step3: Add the fractions

$\frac{12x - 3}{18x^{2}}+\frac{6x^{2}}{18x^{2}}=\frac{6x^{2}+12x - 3}{18x^{2}}=\frac{3(2x^{2}+4x - 1)}{18x^{2}}$.

Step4: Simplify the fraction

$\frac{3(2x^{2}+4x - 1)}{18x^{2}}=\frac{2x^{2}+4x - 1}{6x^{2}}$.

Answer:

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