Algebra Examples

$\frac{a - 2}{8 a} + \frac{2 a + 5}{8 a} - \frac{3 - a}{8 a}$

Step 1

Combine the numerators over the common denominator.

$\frac{a - 2 + 2 a + 5 - (3 - a)}{8 a}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{a - 2 + 2 a + 5 - 1 \cdot 3 - - a}{8 a}$

Step 2.2

Multiply $- 1$ by $3$ .

$\frac{a - 2 + 2 a + 5 - 3 - - a}{8 a}$

Step 2.3

Multiply $- - a$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

$\frac{a - 2 + 2 a + 5 - 3 + 1 a}{8 a}$

Step 2.3.2

Multiply $a$ by $1$ .

$\frac{a - 2 + 2 a + 5 - 3 + a}{8 a}$

$\frac{a - 2 + 2 a + 5 - 3 + a}{8 a}$

$\frac{a - 2 + 2 a + 5 - 3 + a}{8 a}$

Step 3

Simplify terms.

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Step 3.1

Add $a$ and $2 a$ .

$\frac{3 a - 2 + 5 - 3 + a}{8 a}$

Step 3.2

Add $3 a$ and $a$ .

$\frac{4 a - 2 + 5 - 3}{8 a}$

Step 3.3

Add $- 2$ and $5$ .

$\frac{4 a + 3 - 3}{8 a}$

Step 3.4

Combine the opposite terms in $4 a + 3 - 3$ .

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Step 3.4.1

Subtract $3$ from $3$ .

$\frac{4 a + 0}{8 a}$

Step 3.4.2

Add $4 a$ and $0$ .

$\frac{4 a}{8 a}$

$\frac{4 a}{8 a}$

Step 3.5

Cancel the common factor of $4$ and $8$ .

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Step 3.5.1

Factor $4$ out of $4 a$ .

$\frac{4 (a)}{8 a}$

Step 3.5.2

Cancel the common factors.

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Step 3.5.2.1

Factor $4$ out of $8 a$ .

$\frac{4 (a)}{4 (2 a)}$

Step 3.5.2.2

Cancel the common factor.

$\frac{4 a}{4 (2 a)}$

Step 3.5.2.3

Rewrite the expression.

$\frac{a}{2 a}$

$\frac{a}{2 a}$

$\frac{a}{2 a}$

Step 3.6

Cancel the common factor of $a$ .

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Step 3.6.1

Cancel the common factor.

$\frac{a}{2 a}$

Step 3.6.2

Rewrite the expression.

$\frac{1}{2}$

$\frac{1}{2}$

$\frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$