Question

add the rational expressions and write the answer in simplest form $\frac{2y}{8xy}+\frac{5}{3y}$
$\frac{2y + 5x}{8xy}$
$\frac{3y + 20x}{12xy}$
$\frac{2y^{2}+5xy^{2}}{8xy^{2}}$
$\frac{3xy^{2}+20xy^{2}}{12xy^{2}}$

Explanation:

Step1: Find common denominator

The denominators are $8xy$ and $3y$. The least - common denominator (LCD) of $8xy$ and $3y$ is $24xy$.

Step2: Rewrite fractions with LCD

$\frac{2y}{8xy}=\frac{2y\times3}{8xy\times3}=\frac{6y}{24xy}$ and $\frac{5}{3y}=\frac{5\times8x}{3y\times8x}=\frac{40x}{24xy}$.

Step3: Add the fractions

$\frac{6y}{24xy}+\frac{40x}{24xy}=\frac{6y + 40x}{24xy}=\frac{2(3y + 20x)}{24xy}=\frac{3y+20x}{12xy}$

Answer:

$\frac{3y + 20x}{12xy}$