Solve {left(frac{5/2right)}^2+{left(3/2right)}^2-4}{15/2}

$$\frac{ { \left( \frac{ 5 }{ 2 } \right) }^{ 2 } + { \left( \frac{ 3 }{ 2 } \right) }^{ 2 } -4 }{ \frac{ 15 }{ 2 } }$$

Evaluate

$$\frac{3}{5}=0.6$$

Solution Steps

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{\frac{25}{4}+\left(\frac{3}{2}\right)^{2}-4}{\frac{15}{2}}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{\frac{25}{4}+\frac{9}{4}-4}{\frac{15}{2}}$$

Since \frac{25}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25+9}{4}-4}{\frac{15}{2}}$$

Add 25 and 9 to get 34.

$$\frac{\frac{34}{4}-4}{\frac{15}{2}}$$

Reduce the fraction \frac{34}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{17}{2}-4}{\frac{15}{2}}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{\frac{17}{2}-\frac{8}{2}}{\frac{15}{2}}$$

Since \frac{17}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{17-8}{2}}{\frac{15}{2}}$$

Subtract 8 from 17 to get 9.

$$\frac{\frac{9}{2}}{\frac{15}{2}}$$

Divide \frac{9}{2} by \frac{15}{2} by multiplying \frac{9}{2} by the reciprocal of \frac{15}{2}.

$$\frac{9}{2}\times \frac{2}{15}$$

Multiply \frac{9}{2} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 2}{2\times 15}$$

Cancel out 2 in both numerator and denominator.

$$\frac{9}{15}$$

Reduce the fraction \frac{9}{15} to lowest terms by extracting and canceling out 3.

$$\frac{3}{5}$$

Factor

$$\frac{3}{5} = 0.6$$