Question

add the rational expressions and write the answer in simplest form. $\frac{2x - 1}{8x}+\frac{3x + 1}{2x^{2}}$. $\frac{14x + 3}{8x}$, $\frac{2x^{2}+2x + 1}{2x}$, $\frac{2x^{2}+11x + 4}{8x^{2}}$, $\frac{5x}{2x^{2}}$

Explanation:

Step1: Find common denominator

The denominators are $8x$ and $2x^{2}$. The least - common denominator (LCD) is $8x^{2}$.

Step2: Rewrite fractions with LCD

$\frac{2x - 1}{8x}=\frac{(2x - 1)\cdot x}{8x\cdot x}=\frac{2x^{2}-x}{8x^{2}}$ and $\frac{3x + 1}{2x^{2}}=\frac{(3x + 1)\cdot4}{2x^{2}\cdot4}=\frac{12x + 4}{8x^{2}}$.

Step3: Add the fractions

$\frac{2x^{2}-x}{8x^{2}}+\frac{12x + 4}{8x^{2}}=\frac{2x^{2}-x+12x + 4}{8x^{2}}=\frac{2x^{2}+11x + 4}{8x^{2}}$.

Answer:

$\frac{2x^{2}+11x + 4}{8x^{2}}$