Simplify (3x)/(4y^2)-y/(6x)

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

Step 1

To write $\frac{3 x}{4 y^{2}}$ as a fraction with a common denominator, multiply by $\frac{3 x}{3 x}$ .

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $12 x y^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{4 y^{2}}$ by $\frac{3 x}{3 x}$ .

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

Multiply $3$ by $4$ .

$\frac{3 x (3 x)}{12 y^{2} x} - \frac{y}{6 x} \cdot \frac{2 y^{2}}{2 y^{2}}$

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

$\frac{3 x (3 x)}{12 y^{2} x} - \frac{y (2 y^{2})}{6 x (2 y^{2})}$

Multiply $2$ by $6$ .

$\frac{3 x (3 x)}{12 y^{2} x} - \frac{y (2 y^{2})}{12 x y^{2}}$

Reorder the factors of $12 x y^{2}$ .

$\frac{3 x (3 x)}{12 y^{2} x} - \frac{y (2 y^{2})}{12 y^{2} x}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 x (3 x) - y (2 y^{2})}{12 y^{2} x}$

Step 5

Simplify the numerator.

Rewrite using the commutative property of multiplication.

$\frac{3 \cdot 3 x \cdot x - y (2 y^{2})}{12 y^{2} x}$

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

Move $x$ .

$\frac{3 \cdot 3 (x \cdot x) - y (2 y^{2})}{12 y^{2} x}$

Multiply $x$ by $x$ .

$\frac{3 \cdot 3 x^{2} - y (2 y^{2})}{12 y^{2} x}$

Multiply $3$ by $3$ .

$\frac{9 x^{2} - y (2 y^{2})}{12 y^{2} x}$

Rewrite using the commutative property of multiplication.

$\frac{9 x^{2} - 1 \cdot 2 y \cdot y^{2}}{12 y^{2} x}$

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

Move $y^{2}$ .

$\frac{9 x^{2} - 1 \cdot 2 (y^{2} y)}{12 y^{2} x}$

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

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

$\frac{9 x^{2} - 1 \cdot 2 (y^{2} y^{1})}{12 y^{2} x}$

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

$\frac{9 x^{2} - 1 \cdot 2 y^{2 + 1}}{12 y^{2} x}$

Add $2$ and $1$ .

$\frac{9 x^{2} - 1 \cdot 2 y^{3}}{12 y^{2} x}$

Multiply $- 1$ by $2$ .

$\frac{9 x^{2} - 2 y^{3}}{12 y^{2} x}$

Simplify (3x)/(4y^2)-y/(6x)

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