Solve (5/3)^2+1/2*frac{5{3}+1}

$$\frac { ( \frac { 5 } { 3 } ) ^ { 2 } + 1 } { 2 \times \frac { 5 } { 3 } + 1 }$$

Evaluate

$$\frac{34}{39}\approx 0.871794872$$

Solution Steps

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{\frac{25}{9}+1}{2\times \frac{5}{3}+1}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{\frac{25}{9}+\frac{9}{9}}{2\times \frac{5}{3}+1}$$

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

$$\frac{\frac{25+9}{9}}{2\times \frac{5}{3}+1}$$

Add 25 and 9 to get 34.

$$\frac{\frac{34}{9}}{2\times \frac{5}{3}+1}$$

Express 2\times \frac{5}{3} as a single fraction.

$$\frac{\frac{34}{9}}{\frac{2\times 5}{3}+1}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{34}{9}}{\frac{10}{3}+1}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{34}{9}}{\frac{10}{3}+\frac{3}{3}}$$

Since \frac{10}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{34}{9}}{\frac{10+3}{3}}$$

Add 10 and 3 to get 13.

$$\frac{\frac{34}{9}}{\frac{13}{3}}$$

Divide \frac{34}{9} by \frac{13}{3} by multiplying \frac{34}{9} by the reciprocal of \frac{13}{3}.

$$\frac{34}{9}\times \frac{3}{13}$$

Multiply \frac{34}{9} times \frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{34\times 3}{9\times 13}$$

Do the multiplications in the fraction \frac{34\times 3}{9\times 13}.

$$\frac{102}{117}$$

Reduce the fraction \frac{102}{117} to lowest terms by extracting and canceling out 3.

$$\frac{34}{39}$$

Factor

$$\frac{2 \cdot 17}{3 \cdot 13} = 0.8717948717948718$$