Solve y-4/y/frac{4{y}+2}

$$\frac { y - \frac { 4 } { y } } { \frac { 4 } { y } + 2 }$$

Evaluate

$$\frac{y}{2}-1$$

Short Solution Steps

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

$$\frac{\frac{yy}{y}-\frac{4}{y}}{\frac{4}{y}+2}$$

Since \frac{yy}{y} and \frac{4}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{yy-4}{y}}{\frac{4}{y}+2}$$

Do the multiplications in yy-4.

$$\frac{\frac{y^{2}-4}{y}}{\frac{4}{y}+2}$$

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

$$\frac{\frac{y^{2}-4}{y}}{\frac{4}{y}+\frac{2y}{y}}$$

Since \frac{4}{y} and \frac{2y}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{2}-4}{y}}{\frac{4+2y}{y}}$$

Divide \frac{y^{2}-4}{y} by \frac{4+2y}{y} by multiplying \frac{y^{2}-4}{y} by the reciprocal of \frac{4+2y}{y}.

$$\frac{\left(y^{2}-4\right)y}{y\left(4+2y\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{y^{2}-4}{2y+4}$$

Factor the expressions that are not already factored.

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

Cancel out y+2 in both numerator and denominator.

$$\frac{y-2}{2}$$

Expand

$$\frac{y}{2}-1$$

Short Solution Steps

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

$$\frac{\frac{yy}{y}-\frac{4}{y}}{\frac{4}{y}+2}$$

Since \frac{yy}{y} and \frac{4}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{yy-4}{y}}{\frac{4}{y}+2}$$

Do the multiplications in yy-4.

$$\frac{\frac{y^{2}-4}{y}}{\frac{4}{y}+2}$$

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

$$\frac{\frac{y^{2}-4}{y}}{\frac{4}{y}+\frac{2y}{y}}$$

Since \frac{4}{y} and \frac{2y}{y} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{2}-4}{y}}{\frac{4+2y}{y}}$$

Divide \frac{y^{2}-4}{y} by \frac{4+2y}{y} by multiplying \frac{y^{2}-4}{y} by the reciprocal of \frac{4+2y}{y}.

$$\frac{\left(y^{2}-4\right)y}{y\left(4+2y\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{y^{2}-4}{2y+4}$$

Factor the expressions that are not already factored.

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

Cancel out y+2 in both numerator and denominator.

$$\frac{y-2}{2}$$