Simplify (9x^2)/(10y)+(5y^2)/(3x)

$\frac{9 x^{2}}{10 y} + \frac{5 y^{2}}{3 x}$

To write $\frac{9 x^{2}}{10 y}$ as a fraction with a common denominator, multiply by $\frac{3 x}{3 x}$ .

$\frac{9 x^{2}}{10 y} \cdot \frac{3 x}{3 x} + \frac{5 y^{2}}{3 x}$

To write $\frac{5 y^{2}}{3 x}$ as a fraction with a common denominator, multiply by $\frac{10 y}{10 y}$ .

$\frac{9 x^{2}}{10 y} \cdot \frac{3 x}{3 x} + \frac{5 y^{2}}{3 x} \cdot \frac{10 y}{10 y}$

Write each expression with a common denominator of $30 y x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9 x^{2}}{10 y}$ by $\frac{3 x}{3 x}$ .

$\frac{9 x^{2} (3 x)}{10 y (3 x)} + \frac{5 y^{2}}{3 x} \cdot \frac{10 y}{10 y}$

Multiply $3$ by $10$ .

$\frac{9 x^{2} (3 x)}{30 y x} + \frac{5 y^{2}}{3 x} \cdot \frac{10 y}{10 y}$

Multiply $\frac{5 y^{2}}{3 x}$ by $\frac{10 y}{10 y}$ .

$\frac{9 x^{2} (3 x)}{30 y x} + \frac{5 y^{2} (10 y)}{3 x (10 y)}$

Multiply $10$ by $3$ .

$\frac{9 x^{2} (3 x)}{30 y x} + \frac{5 y^{2} (10 y)}{30 x y}$

Reorder the factors of $30 y x$ .

$\frac{9 x^{2} (3 x)}{30 x y} + \frac{5 y^{2} (10 y)}{30 x y}$

Combine the numerators over the common denominator.

$\frac{9 x^{2} (3 x) + 5 y^{2} (10 y)}{30 x y}$

Simplify the numerator.

Rewrite using the commutative property of multiplication.

$\frac{9 \cdot 3 x^{2} x + 5 y^{2} (10 y)}{30 x y}$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$\frac{9 \cdot 3 (x \cdot x^{2}) + 5 y^{2} (10 y)}{30 x y}$

Multiply $x$ by $x^{2}$ .

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

$\frac{9 \cdot 3 (x^{1} x^{2}) + 5 y^{2} (10 y)}{30 x y}$

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

$\frac{9 \cdot 3 x^{1 + 2} + 5 y^{2} (10 y)}{30 x y}$

Add $1$ and $2$ .

$\frac{9 \cdot 3 x^{3} + 5 y^{2} (10 y)}{30 x y}$

Multiply $9$ by $3$ .

$\frac{27 x^{3} + 5 y^{2} (10 y)}{30 x y}$

Rewrite using the commutative property of multiplication.

$\frac{27 x^{3} + 5 \cdot 10 y^{2} y}{30 x y}$

Multiply $y^{2}$ by $y$ by adding the exponents.

Move $y$ .

$\frac{27 x^{3} + 5 \cdot 10 (y \cdot y^{2})}{30 x y}$

Multiply $y$ by $y^{2}$ .

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

$\frac{27 x^{3} + 5 \cdot 10 (y^{1} y^{2})}{30 x y}$

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

$\frac{27 x^{3} + 5 \cdot 10 y^{1 + 2}}{30 x y}$

Add $1$ and $2$ .

$\frac{27 x^{3} + 5 \cdot 10 y^{3}}{30 x y}$

Multiply $5$ by $10$ .

$\frac{27 x^{3} + 50 y^{3}}{30 x y}$

Simplify (9x^2)/(10y)+(5y^2)/(3x)

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