Precalculus Examples

$\frac{23 x}{y^{2}} - \frac{16 y}{x}$

Step 1

To write $\frac{23 x}{y^{2}}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{23 x}{y^{2}} \cdot \frac{x}{x} - \frac{16 y}{x}$

Step 2

To write $- \frac{16 y}{x}$ as a fraction with a common denominator, multiply by $\frac{y^{2}}{y^{2}}$ .

$\frac{23 x}{y^{2}} \cdot \frac{x}{x} - \frac{16 y}{x} \cdot \frac{y^{2}}{y^{2}}$

Step 3

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

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Step 3.1

Multiply $\frac{23 x}{y^{2}}$ by $\frac{x}{x}$ .

$\frac{23 x \cdot x}{y^{2} x} - \frac{16 y}{x} \cdot \frac{y^{2}}{y^{2}}$

Step 3.2

Multiply $\frac{16 y}{x}$ by $\frac{y^{2}}{y^{2}}$ .

$\frac{23 x \cdot x}{y^{2} x} - \frac{16 y \cdot y^{2}}{x y^{2}}$

Step 3.3

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

$\frac{23 x \cdot x}{y^{2} x} - \frac{16 y \cdot y^{2}}{y^{2} x}$

Step 4

Combine the numerators over the common denominator.

$\frac{23 x \cdot x - 16 y \cdot y^{2}}{y^{2} x}$

Step 5

Simplify the numerator.

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Step 5.1

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

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Step 5.1.1

Move $x$ .

$\frac{23 (x \cdot x) - 16 y \cdot y^{2}}{y^{2} x}$

Step 5.1.2

Multiply $x$ by $x$ .

$\frac{23 x^{2} - 16 y \cdot y^{2}}{y^{2} x}$

Step 5.2

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

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Step 5.2.1

Move $y^{2}$ .

$\frac{23 x^{2} - 16 (y^{2} y)}{y^{2} x}$

Step 5.2.2

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

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Step 5.2.2.1

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

$\frac{23 x^{2} - 16 (y^{2} y^{1})}{y^{2} x}$

Step 5.2.2.2

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

$\frac{23 x^{2} - 16 y^{2 + 1}}{y^{2} x}$

Step 5.2.3

Add $2$ and $1$ .

$\frac{23 x^{2} - 16 y^{3}}{y^{2} x}$