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

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

Step 1

Simplify each term.

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 y$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $5 x^{2} y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

$\frac{3 x}{5 (x^{1} x) y^{2}} + \frac{2}{x^{2}} \cdot \frac{5 y^{2}}{5 y^{2}}$

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

$\frac{3 x}{5 (x^{1} x^{1}) y^{2}} + \frac{2}{x^{2}} \cdot \frac{5 y^{2}}{5 y^{2}}$

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

$\frac{3 x}{5 x^{1 + 1} y^{2}} + \frac{2}{x^{2}} \cdot \frac{5 y^{2}}{5 y^{2}}$

Add $1$ and $1$ .

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

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

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

Reorder the factors of $x^{2} (5 y^{2})$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Multiply $2$ by $5$ .

$\frac{3 x + 10 y^{2}}{5 x^{2} y^{2}}$

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

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