Simplify (3y)/(2y^2-y)+2/(2y)

$\frac{3 y}{2 y^{2} - y} + \frac{2}{2 y}$

Step 1

Simplify each term.

Factor $y$ out of $2 y^{2} - y$ .

Factor $y$ out of $2 y^{2}$ .

$\frac{3 y}{y (2 y) - y} + \frac{2}{2 y}$

Factor $y$ out of $- y$ .

$\frac{3 y}{y (2 y) + y \cdot - 1} + \frac{2}{2 y}$

Factor $y$ out of $y (2 y) + y \cdot - 1$ .

$\frac{3 y}{y (2 y - 1)} + \frac{2}{2 y}$

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{3 y}{y (2 y - 1)} + \frac{2}{2 y}$

Rewrite the expression.

$\frac{3}{2 y - 1} + \frac{2}{2 y}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3}{2 y - 1} + \frac{2}{2 y}$

Rewrite the expression.

$\frac{3}{2 y - 1} + \frac{1}{y}$

Step 2

To write $\frac{3}{2 y - 1}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{3}{2 y - 1} \cdot \frac{y}{y} + \frac{1}{y}$

Step 3

To write $\frac{1}{y}$ as a fraction with a common denominator, multiply by $\frac{2 y - 1}{2 y - 1}$ .

$\frac{3}{2 y - 1} \cdot \frac{y}{y} + \frac{1}{y} \cdot \frac{2 y - 1}{2 y - 1}$

Step 4

Write each expression with a common denominator of $(2 y - 1) y$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2 y - 1}$ by $\frac{y}{y}$ .

$\frac{3 y}{(2 y - 1) y} + \frac{1}{y} \cdot \frac{2 y - 1}{2 y - 1}$

Multiply $\frac{1}{y}$ by $\frac{2 y - 1}{2 y - 1}$ .

$\frac{3 y}{(2 y - 1) y} + \frac{2 y - 1}{y (2 y - 1)}$

Reorder the factors of $(2 y - 1) y$ .

$\frac{3 y}{y (2 y - 1)} + \frac{2 y - 1}{y (2 y - 1)}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 y + 2 y - 1}{y (2 y - 1)}$

Step 6

Add $3 y$ and $2 y$ .

$\frac{5 y - 1}{y (2 y - 1)}$