Algebra Examples

$\frac{{(\frac{5}{2})}^{2} + \frac{5}{2}}{\frac{5}{2} - 1}$

Step 1

Multiply the numerator and denominator of the fraction by $2$ .

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Step 1.1

Multiply $\frac{{(\frac{5}{2})}^{2} + \frac{5}{2}}{\frac{5}{2} - 1}$ by $\frac{2}{2}$ .

$\frac{2}{2} \cdot \frac{{(\frac{5}{2})}^{2} + \frac{5}{2}}{\frac{5}{2} - 1}$

Step 1.2

Combine.

$\frac{2 ({(\frac{5}{2})}^{2} + \frac{5}{2})}{2 (\frac{5}{2} - 1)}$

Step 2

Apply the distributive property.

$\frac{2 {(\frac{5}{2})}^{2} + 2 (\frac{5}{2})}{2 (\frac{5}{2}) + 2 \cdot - 1}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Cancel the common factor.

$\frac{2 {(\frac{5}{2})}^{2} + 2 (\frac{5}{2})}{2 (\frac{5}{2}) + 2 \cdot - 1}$

Step 3.1.2

Rewrite the expression.

$\frac{2 {(\frac{5}{2})}^{2} + 5}{2 (\frac{5}{2}) + 2 \cdot - 1}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Cancel the common factor.

$\frac{2 {(\frac{5}{2})}^{2} + 5}{2 (\frac{5}{2}) + 2 \cdot - 1}$

Step 3.2.2

Rewrite the expression.

$\frac{2 {(\frac{5}{2})}^{2} + 5}{5 + 2 \cdot - 1}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the product rule to $\frac{5}{2}$ .

$\frac{2 \frac{5^{2}}{2^{2}} + 5}{5 + 2 \cdot - 1}$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

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

$\frac{2 \frac{5^{2}}{2 \cdot 2} + 5}{5 + 2 \cdot - 1}$

Step 4.2.2

Cancel the common factor.

$\frac{2 \frac{5^{2}}{2 \cdot 2} + 5}{5 + 2 \cdot - 1}$

Step 4.2.3

Rewrite the expression.

$\frac{\frac{5^{2}}{2} + 5}{5 + 2 \cdot - 1}$

Step 4.3

Raise $5$ to the power of $2$ .

$\frac{\frac{25}{2} + 5}{5 + 2 \cdot - 1}$

Step 4.4

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{25}{2} + 5 \cdot \frac{2}{2}}{5 + 2 \cdot - 1}$

Step 4.5

Combine $5$ and $\frac{2}{2}$ .

$\frac{\frac{25}{2} + \frac{5 \cdot 2}{2}}{5 + 2 \cdot - 1}$

Step 4.6

Combine the numerators over the common denominator.

$\frac{\frac{25 + 5 \cdot 2}{2}}{5 + 2 \cdot - 1}$

Step 4.7

Simplify the numerator.

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Step 4.7.1

Multiply $5$ by $2$ .

$\frac{\frac{25 + 10}{2}}{5 + 2 \cdot - 1}$

Step 4.7.2

Add $25$ and $10$ .

$\frac{\frac{35}{2}}{5 + 2 \cdot - 1}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $2$ by $- 1$ .

$\frac{\frac{35}{2}}{5 - 2}$

Step 5.2

Subtract $2$ from $5$ .

$\frac{\frac{35}{2}}{3}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{35}{2} \cdot \frac{1}{3}$

Step 7

Multiply $\frac{35}{2} \cdot \frac{1}{3}$ .

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Step 7.1

Multiply $\frac{35}{2}$ by $\frac{1}{3}$ .

$\frac{35}{2 \cdot 3}$

Step 7.2

Multiply $2$ by $3$ .

$\frac{35}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{6}$

Decimal Form:

$5.8\overline{3}$

Mixed Number Form:

$5 \frac{5}{6}$