Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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Step 2.2.1.1

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

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

Step 2.2.1.2

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

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

Step 2.2.2

Add $2$ and $1$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

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

Step 4.2

Multiply $- 1$ by $1$ .

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

Step 4.3

Apply the distributive property.

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

Step 4.4

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

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Step 4.4.1

Move $x$ .

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

Step 4.4.2

Multiply $x$ by $x$ .

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

Step 4.5

Rewrite $- 1 x$ as $- x$ .

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

Step 4.6

Subtract $x$ from $x$ .

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

Step 4.7

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

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