Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

Add $4$ and $2$ .

$(3 + 4) - \frac{4}{4 - 2} + \frac{3 \cdot 6}{3}$

Step 1.2

Multiply $3$ by $6$ .

$(3 + 4) - \frac{4}{4 - 2} + \frac{18}{3}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $4$ and $4 - 2$ .

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Step 2.1.1

Factor $2$ out of $4$ .

$3 + 4 - \frac{2 (2)}{4 - 2} + \frac{18}{3}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $4$ .

$3 + 4 - \frac{2 \cdot 2}{2 \cdot 2 - 2} + \frac{18}{3}$

Step 2.1.2.2

Factor $2$ out of $- 2$ .

$3 + 4 - \frac{2 (2)}{2 \cdot 2 + 2 \cdot - 1} + \frac{18}{3}$

Step 2.1.2.3

Factor $2$ out of $2 \cdot 2 + 2 \cdot - 1$ .

$3 + 4 - \frac{2 (2)}{2 \cdot (2 - 1)} + \frac{18}{3}$

Step 2.1.2.4

Cancel the common factor.

$3 + 4 - \frac{2 \cdot 2}{2 \cdot (2 - 1)} + \frac{18}{3}$

Step 2.1.2.5

Rewrite the expression.

$3 + 4 - \frac{2}{2 - 1} + \frac{18}{3}$

Step 2.2

Subtract $1$ from $2$ .

$3 + 4 - \frac{2}{1} + \frac{18}{3}$

Step 2.3

Divide $2$ by $1$ .

$3 + 4 - 1 \cdot 2 + \frac{18}{3}$

Step 2.4

Multiply $- 1$ by $2$ .

$3 + 4 - 2 + \frac{18}{3}$

Step 2.5

Divide $18$ by $3$ .

$3 + 4 - 2 + 6$

Step 3

Simplify by adding and subtracting.

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Step 3.1

Add $3$ and $4$ .

$7 - 2 + 6$

Step 3.2

Subtract $2$ from $7$ .

$5 + 6$

Step 3.3

Add $5$ and $6$ .

$11$