Trigonometry Examples

$\frac{3}{8 x^{3} y^{3}} - \frac{1}{4 x y}$

Step 1

To write $- \frac{1}{4 x y}$ as a fraction with a common denominator, multiply by $\frac{2 x^{2} y^{2}}{2 x^{2} y^{2}}$ .

$\frac{3}{8 x^{3} y^{3}} - \frac{1}{4 x y} \cdot \frac{2 x^{2} y^{2}}{2 x^{2} y^{2}}$

Step 2

Write each expression with a common denominator of $8 x^{3} y^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{1}{4 x y}$ by $\frac{2 x^{2} y^{2}}{2 x^{2} y^{2}}$ .

$\frac{3}{8 x^{3} y^{3}} - \frac{2 x^{2} y^{2}}{4 x y (2 x^{2} y^{2})}$

Step 2.2

Multiply $2$ by $4$ .

$\frac{3}{8 x^{3} y^{3}} - \frac{2 x^{2} y^{2}}{8 x y (x^{2} y^{2})}$

Step 2.3

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

$\frac{3}{8 x^{3} y^{3}} - \frac{2 x^{2} y^{2}}{8 (x^{2} x^{1}) y \cdot y^{2}}$

Step 2.4

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

$\frac{3}{8 x^{3} y^{3}} - \frac{2 x^{2} y^{2}}{8 x^{2 + 1} y \cdot y^{2}}$

Step 2.5

Add $2$ and $1$ .

$\frac{3}{8 x^{3} y^{3}} - \frac{2 x^{2} y^{2}}{8 x^{3} y \cdot y^{2}}$

Step 2.6

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

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Step 2.6.1

Move $y^{2}$ .

$\frac{3}{8 x^{3} y^{3}} - \frac{2 x^{2} y^{2}}{8 x^{3} (y^{2} y)}$

Step 2.6.2

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

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Step 2.6.2.1

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

$\frac{3}{8 x^{3} y^{3}} - \frac{2 x^{2} y^{2}}{8 x^{3} (y^{2} y^{1})}$

Step 2.6.2.2

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

$\frac{3}{8 x^{3} y^{3}} - \frac{2 x^{2} y^{2}}{8 x^{3} y^{2 + 1}}$

Step 2.6.3

Add $2$ and $1$ .

$\frac{3}{8 x^{3} y^{3}} - \frac{2 x^{2} y^{2}}{8 x^{3} y^{3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 - 2 x^{2} y^{2}}{8 x^{3} y^{3}}$