Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify the denominator.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Reorder terms.

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

Step 2.3

Add $1$ and $1$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

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

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

Step 5

Cancel the common factor of $x$ .

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Step 5.1

Factor $x$ out of $x^{2}$ .

$\frac{x + 1}{x \cdot x} \cdot \frac{x}{x + 2}$

Step 5.2

Cancel the common factor.

$\frac{x + 1}{x \cdot x} \cdot \frac{x}{x + 2}$

Step 5.3

Rewrite the expression.

$\frac{x + 1}{x} \cdot \frac{1}{x + 2}$

Step 6

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

$\frac{x + 1}{x (x + 2)}$