Simplify (12y)/(5x)+(5x)/(4y^3)

$\frac{12 y}{5 x} + \frac{5 x}{4 y^{3}}$

To write $\frac{12 y}{5 x}$ as a fraction with a common denominator, multiply by $\frac{4 y^{3}}{4 y^{3}}$ .

$\frac{12 y}{5 x} \cdot \frac{4 y^{3}}{4 y^{3}} + \frac{5 x}{4 y^{3}}$

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

$\frac{12 y}{5 x} \cdot \frac{4 y^{3}}{4 y^{3}} + \frac{5 x}{4 y^{3}} \cdot \frac{5 x}{5 x}$

Write each expression with a common denominator of $20 x y^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{12 y}{5 x}$ by $\frac{4 y^{3}}{4 y^{3}}$ .

$\frac{12 y (4 y^{3})}{5 x (4 y^{3})} + \frac{5 x}{4 y^{3}} \cdot \frac{5 x}{5 x}$

Multiply $4$ by $5$ .

$\frac{12 y (4 y^{3})}{20 x y^{3}} + \frac{5 x}{4 y^{3}} \cdot \frac{5 x}{5 x}$

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

$\frac{12 y (4 y^{3})}{20 x y^{3}} + \frac{5 x (5 x)}{4 y^{3} (5 x)}$

Multiply $5$ by $4$ .

$\frac{12 y (4 y^{3})}{20 x y^{3}} + \frac{5 x (5 x)}{20 y^{3} x}$

Reorder the factors of $20 x y^{3}$ .

$\frac{12 y (4 y^{3})}{20 y^{3} x} + \frac{5 x (5 x)}{20 y^{3} x}$

Combine the numerators over the common denominator.

$\frac{12 y (4 y^{3}) + 5 x (5 x)}{20 y^{3} x}$

Simplify the numerator.

Rewrite using the commutative property of multiplication.

$\frac{12 \cdot 4 y \cdot y^{3} + 5 x (5 x)}{20 y^{3} x}$

Multiply $y$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$\frac{12 \cdot 4 (y^{3} y) + 5 x (5 x)}{20 y^{3} x}$

Multiply $y^{3}$ by $y$ .

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

$\frac{12 \cdot 4 (y^{3} y^{1}) + 5 x (5 x)}{20 y^{3} x}$

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

$\frac{12 \cdot 4 y^{3 + 1} + 5 x (5 x)}{20 y^{3} x}$

Add $3$ and $1$ .

$\frac{12 \cdot 4 y^{4} + 5 x (5 x)}{20 y^{3} x}$

Multiply $12$ by $4$ .

$\frac{48 y^{4} + 5 x (5 x)}{20 y^{3} x}$

Rewrite using the commutative property of multiplication.

$\frac{48 y^{4} + 5 \cdot 5 x \cdot x}{20 y^{3} x}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{48 y^{4} + 5 \cdot 5 (x \cdot x)}{20 y^{3} x}$

Multiply $x$ by $x$ .

$\frac{48 y^{4} + 5 \cdot 5 x^{2}}{20 y^{3} x}$

Multiply $5$ by $5$ .

$\frac{48 y^{4} + 25 x^{2}}{20 y^{3} x}$