Solve y-2y-5/5/frac{15{10}+5/2y}

$$\frac { y - \frac { 2 y - 5 } { 5 } } { \frac { 15 } { 10 } + \frac { 5 } { 2 y } }$$

Evaluate

$$\frac{2y}{5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{5}{5}.

$$\frac{\frac{5y}{5}-\frac{2y-5}{5}}{\frac{15}{10}+\frac{5}{2y}}$$

Since \frac{5y}{5} and \frac{2y-5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5y-\left(2y-5\right)}{5}}{\frac{15}{10}+\frac{5}{2y}}$$

Do the multiplications in 5y-\left(2y-5\right).

$$\frac{\frac{5y-2y+5}{5}}{\frac{15}{10}+\frac{5}{2y}}$$

Combine like terms in 5y-2y+5.

$$\frac{\frac{3y+5}{5}}{\frac{15}{10}+\frac{5}{2y}}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{3y+5}{5}}{\frac{3}{2}+\frac{5}{2y}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2y is 2y. Multiply \frac{3}{2} times \frac{y}{y}.

$$\frac{\frac{3y+5}{5}}{\frac{3y}{2y}+\frac{5}{2y}}$$

Since \frac{3y}{2y} and \frac{5}{2y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3y+5}{5}}{\frac{3y+5}{2y}}$$

Divide \frac{3y+5}{5} by \frac{3y+5}{2y} by multiplying \frac{3y+5}{5} by the reciprocal of \frac{3y+5}{2y}.

$$\frac{\left(3y+5\right)\times 2y}{5\left(3y+5\right)}$$

Cancel out 3y+5 in both numerator and denominator.

$$\frac{2y}{5}$$

Expand

$$\frac{2y}{5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{5}{5}.

$$\frac{\frac{5y}{5}-\frac{2y-5}{5}}{\frac{15}{10}+\frac{5}{2y}}$$

Since \frac{5y}{5} and \frac{2y-5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5y-\left(2y-5\right)}{5}}{\frac{15}{10}+\frac{5}{2y}}$$

Do the multiplications in 5y-\left(2y-5\right).

$$\frac{\frac{5y-2y+5}{5}}{\frac{15}{10}+\frac{5}{2y}}$$

Combine like terms in 5y-2y+5.

$$\frac{\frac{3y+5}{5}}{\frac{15}{10}+\frac{5}{2y}}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{3y+5}{5}}{\frac{3}{2}+\frac{5}{2y}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2y is 2y. Multiply \frac{3}{2} times \frac{y}{y}.

$$\frac{\frac{3y+5}{5}}{\frac{3y}{2y}+\frac{5}{2y}}$$

Since \frac{3y}{2y} and \frac{5}{2y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3y+5}{5}}{\frac{3y+5}{2y}}$$

Divide \frac{3y+5}{5} by \frac{3y+5}{2y} by multiplying \frac{3y+5}{5} by the reciprocal of \frac{3y+5}{2y}.

$$\frac{\left(3y+5\right)\times 2y}{5\left(3y+5\right)}$$

Cancel out 3y+5 in both numerator and denominator.

$$\frac{2y}{5}$$