Algebra Examples

$\frac{x + 1}{3 x^{2} + 6 x} - \frac{1 - 2 x}{3 x^{2} + 6 x}$

Step 1

Combine the numerators over the common denominator.

$\frac{x + 1 - (1 - 2 x)}{3 x^{2} + 6 x}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{x + 1 - 1 \cdot 1 - (- 2 x)}{3 x^{2} + 6 x}$

Step 2.2

Multiply $- 1$ by $1$ .

$\frac{x + 1 - 1 - (- 2 x)}{3 x^{2} + 6 x}$

Step 2.3

Multiply $- 2$ by $- 1$ .

$\frac{x + 1 - 1 + 2 x}{3 x^{2} + 6 x}$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $x + 1 - 1 + 2 x$ .

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Step 3.1.1

Subtract $1$ from $1$ .

$\frac{x + 0 + 2 x}{3 x^{2} + 6 x}$

Step 3.1.2

Add $x$ and $0$ .

$\frac{x + 2 x}{3 x^{2} + 6 x}$

Step 3.2

Add $x$ and $2 x$ .

$\frac{3 x}{3 x^{2} + 6 x}$

Step 3.3

Factor $3 x$ out of $3 x^{2} + 6 x$ .

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Step 3.3.1

Factor $3 x$ out of $3 x^{2}$ .

$\frac{3 x}{3 x (x) + 6 x}$

Step 3.3.2

Factor $3 x$ out of $6 x$ .

$\frac{3 x}{3 x (x) + 3 x (2)}$

Step 3.3.3

Factor $3 x$ out of $3 x (x) + 3 x (2)$ .

$\frac{3 x}{3 x (x + 2)}$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Cancel the common factor.

$\frac{3 x}{3 x (x + 2)}$

Step 3.4.2

Rewrite the expression.

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

Step 3.5

Cancel the common factor of $x$ .

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Step 3.5.1

Cancel the common factor.

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

Step 3.5.2

Rewrite the expression.

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