Simplify (6y)/(5x^2)+4/(3xy)

$\frac{6 y}{5 x^{2}} + \frac{4}{3 x y}$

To write $\frac{6 y}{5 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{3 y}{3 y}$ .

$\frac{6 y}{5 x^{2}} \cdot \frac{3 y}{3 y} + \frac{4}{3 x y}$

To write $\frac{4}{3 x y}$ as a fraction with a common denominator, multiply by $\frac{5 x}{5 x}$ .

$\frac{6 y}{5 x^{2}} \cdot \frac{3 y}{3 y} + \frac{4}{3 x y} \cdot \frac{5 x}{5 x}$

Write each expression with a common denominator of $15 y x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6 y}{5 x^{2}}$ by $\frac{3 y}{3 y}$ .

$\frac{6 y (3 y)}{5 x^{2} (3 y)} + \frac{4}{3 x y} \cdot \frac{5 x}{5 x}$

Multiply $3$ by $5$ .

$\frac{6 y (3 y)}{15 x^{2} y} + \frac{4}{3 x y} \cdot \frac{5 x}{5 x}$

Multiply $\frac{4}{3 x y}$ by $\frac{5 x}{5 x}$ .

$\frac{6 y (3 y)}{15 x^{2} y} + \frac{4 (5 x)}{3 x y (5 x)}$

Multiply $5$ by $3$ .

$\frac{6 y (3 y)}{15 x^{2} y} + \frac{4 (5 x)}{15 x y x}$

Raise $x$ to the power of $1$ .

$\frac{6 y (3 y)}{15 x^{2} y} + \frac{4 (5 x)}{15 (x^{1} x) y}$

Raise $x$ to the power of $1$ .

$\frac{6 y (3 y)}{15 x^{2} y} + \frac{4 (5 x)}{15 (x^{1} x^{1}) y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6 y (3 y)}{15 x^{2} y} + \frac{4 (5 x)}{15 x^{1 + 1} y}$

Add $1$ and $1$ .

$\frac{6 y (3 y)}{15 x^{2} y} + \frac{4 (5 x)}{15 x^{2} y}$

Combine the numerators over the common denominator.

$\frac{6 y (3 y) + 4 (5 x)}{15 x^{2} y}$

Simplify the numerator.

Factor $2$ out of $6 y (3 y) + 4 \cdot 5 x$ .

Factor $2$ out of $6 y (3 y)$ .

$\frac{2 (3 y (3 y)) + 4 \cdot 5 x}{15 x^{2} y}$

Factor $2$ out of $4 \cdot 5 x$ .

$\frac{2 (3 y (3 y)) + 2 (2 \cdot 5 x)}{15 x^{2} y}$

Factor $2$ out of $2 (3 y (3 y)) + 2 (2 \cdot 5 x)$ .

$\frac{2 (3 y (3 y) + 2 \cdot 5 x)}{15 x^{2} y}$

Rewrite using the commutative property of multiplication.

$\frac{2 (3 \cdot 3 y \cdot y + 2 \cdot 5 x)}{15 x^{2} y}$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$\frac{2 (3 \cdot 3 (y \cdot y) + 2 \cdot 5 x)}{15 x^{2} y}$

Multiply $y$ by $y$ .

$\frac{2 (3 \cdot 3 y^{2} + 2 \cdot 5 x)}{15 x^{2} y}$

Multiply $3$ by $3$ .

$\frac{2 (9 y^{2} + 2 \cdot 5 x)}{15 x^{2} y}$

Multiply $2$ by $5$ .

$\frac{2 (9 y^{2} + 10 x)}{15 x^{2} y}$