Question

simplify \\(\frac{2y}{3x^2} - \frac{5}{y}\\). write your answer as a single rational expression.

Explanation:

Step1: Find a common denominator

The denominators are $3x^2$ and $y$, so the common denominator is $3x^2y$.
Rewrite each fraction with the common denominator:
$\frac{2y}{3x^2}=\frac{2y\times y}{3x^2\times y}=\frac{2y^2}{3x^2y}$
$\frac{5}{y}=\frac{5\times 3x^2}{y\times 3x^2}=\frac{15x^2}{3x^2y}$

Step2: Subtract the fractions

Now that the fractions have the same denominator, subtract them:
$\frac{2y^2}{3x^2y}-\frac{15x^2}{3x^2y}=\frac{2y^2 - 15x^2}{3x^2y}$

Answer:

$\frac{2y^2 - 15x^2}{3x^2y}$