Algebra Examples

$\frac{3 x}{x + 1} \div x + 1$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{\frac{3 x}{x + 1}}{x} + 1$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{3 x}{x + 1} \cdot \frac{1}{x} + 1$

Step 1.3

Cancel the common factor of $x$ .

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Step 1.3.1

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3}{x + 1} \cdot \frac{1}{x} + 1$

Step 1.3.2

Cancel the common factor.

$\frac{x \cdot 3}{x + 1} \cdot \frac{1}{x} + 1$

Step 1.3.3

Rewrite the expression.

$\frac{3}{x + 1} + 1$

Step 2

Combine into one fraction.

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Step 2.1

Write $1$ as a fraction with a common denominator.

$\frac{3}{x + 1} + \frac{x + 1}{x + 1}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{3 + x + 1}{x + 1}$

Step 2.3

Add $3$ and $1$ .

$\frac{x + 4}{x + 1}$