Algebra Examples

$\frac{2 x + 3}{x^{4}} - \frac{x + 2}{x^{3}}$

Step 1

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

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

Step 2

Write each expression with a common denominator of $x^{4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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Step 2.2.1.1

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

$\frac{2 x + 3}{x^{4}} - \frac{(x + 2) x}{x^{3} x^{1}}$

Step 2.2.1.2

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

$\frac{2 x + 3}{x^{4}} - \frac{(x + 2) x}{x^{3 + 1}}$

Step 2.2.2

Add $3$ and $1$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{2 x + 3 + (- x - 1 \cdot 2) x}{x^{4}}$

Step 4.2

Multiply $- 1$ by $2$ .

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

Step 4.3

Apply the distributive property.

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

Step 4.4

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

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Step 4.4.1

Move $x$ .

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

Step 4.4.2

Multiply $x$ by $x$ .

$\frac{2 x + 3 - x^{2} - 2 x}{x^{4}}$

Step 4.5

Subtract $2 x$ from $2 x$ .

$\frac{3 - x^{2} + 0}{x^{4}}$

Step 4.6

Add $3 - x^{2}$ and $0$ .

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