Simplify 6/(5x^2y)+5/(10xy^2)

$\frac{6}{5 x^{2} y} + \frac{5}{10 x y^{2}}$

Step 1

Cancel the common factor of $5$ and $10$ .

Factor $5$ out of $5$ .

$\frac{6}{5 x^{2} y} + \frac{5 (1)}{10 x y^{2}}$

Cancel the common factors.

Factor $5$ out of $10 x y^{2}$ .

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

Cancel the common factor.

$\frac{6}{5 x^{2} y} + \frac{5 \cdot 1}{5 (2 x y^{2})}$

Rewrite the expression.

$\frac{6}{5 x^{2} y} + \frac{1}{2 x y^{2}}$

Step 2

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

$\frac{6}{5 x^{2} y} \cdot \frac{2 y}{2 y} + \frac{1}{2 x y^{2}}$

Step 3

To write $\frac{1}{2 x y^{2}}$ as a fraction with a common denominator, multiply by $\frac{5 x}{5 x}$ .

$\frac{6}{5 x^{2} y} \cdot \frac{2 y}{2 y} + \frac{1}{2 x y^{2}} \cdot \frac{5 x}{5 x}$

Step 4

Write each expression with a common denominator of $10 x^{2} y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{6 (2 y)}{5 x^{2} y (2 y)} + \frac{1}{2 x y^{2}} \cdot \frac{5 x}{5 x}$

Multiply $2$ by $5$ .

$\frac{6 (2 y)}{10 x^{2} y \cdot y} + \frac{1}{2 x y^{2}} \cdot \frac{5 x}{5 x}$

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

$\frac{6 (2 y)}{10 x^{2} (y^{1} y)} + \frac{1}{2 x y^{2}} \cdot \frac{5 x}{5 x}$

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

$\frac{6 (2 y)}{10 x^{2} (y^{1} y^{1})} + \frac{1}{2 x y^{2}} \cdot \frac{5 x}{5 x}$

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

$\frac{6 (2 y)}{10 x^{2} y^{1 + 1}} + \frac{1}{2 x y^{2}} \cdot \frac{5 x}{5 x}$

Add $1$ and $1$ .

$\frac{6 (2 y)}{10 x^{2} y^{2}} + \frac{1}{2 x y^{2}} \cdot \frac{5 x}{5 x}$

Multiply $\frac{1}{2 x y^{2}}$ by $\frac{5 x}{5 x}$ .

$\frac{6 (2 y)}{10 x^{2} y^{2}} + \frac{5 x}{2 x y^{2} (5 x)}$

Multiply $5$ by $2$ .

$\frac{6 (2 y)}{10 x^{2} y^{2}} + \frac{5 x}{10 x y^{2} x}$

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

$\frac{6 (2 y)}{10 x^{2} y^{2}} + \frac{5 x}{10 (x^{1} x) y^{2}}$

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

$\frac{6 (2 y)}{10 x^{2} y^{2}} + \frac{5 x}{10 (x^{1} x^{1}) y^{2}}$

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

$\frac{6 (2 y)}{10 x^{2} y^{2}} + \frac{5 x}{10 x^{1 + 1} y^{2}}$

Add $1$ and $1$ .

$\frac{6 (2 y)}{10 x^{2} y^{2}} + \frac{5 x}{10 x^{2} y^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 (2 y) + 5 x}{10 x^{2} y^{2}}$

Step 6

Multiply $6$ by $2$ .

$\frac{12 y + 5 x}{10 x^{2} y^{2}}$

Simplify 6/(5x^2y)+5/(10xy^2)

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