Solve y/5+2/frac{5{y}+2}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5}{5}.

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

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

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

Do the multiplications in y+2\times 5.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{y}{y}.

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

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

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

Divide \frac{y+10}{5} by \frac{5+2y}{y} by multiplying \frac{y+10}{5} by the reciprocal of \frac{5+2y}{y}.

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

Use the distributive property to multiply y+10 by y.

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

Use the distributive property to multiply 5 by 5+2y.

$$\frac{y^{2}+10y}{25+10y}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5}{5}.

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

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

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

Do the multiplications in y+2\times 5.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{y}{y}.

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

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

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

Divide \frac{y+10}{5} by \frac{5+2y}{y} by multiplying \frac{y+10}{5} by the reciprocal of \frac{5+2y}{y}.

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

Use the distributive property to multiply y+10 by y.

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

Use the distributive property to multiply 5 by 5+2y.

$$\frac{y^{2}+10y}{25+10y}$$