Evaluate ((5/2)^2+5/2)/(5/2-1)

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

Step 1

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

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

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

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.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the numerator.

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

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

Cancel the common factor of $2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $2$ .

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

Add $25$ and $10$ .

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

Step 5

Simplify the denominator.

Multiply $2$ by $- 1$ .

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

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

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

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

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:

$5 \frac{5}{6}$

Evaluate ((5/2)^2+5/2)/(5/2-1)

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