Solve 6-y/6/frac{1{6}-1/y}

$$\frac { \frac { 6 - y } { 6 } } { \frac { 1 } { 6 } - \frac { 1 } { y } }$$

Evaluate

$$-y$$

Solution Steps

Express \frac{\frac{6-y}{6}}{\frac{1}{6}-\frac{1}{y}} as a single fraction.

$$\frac{6-y}{6\left(\frac{1}{6}-\frac{1}{y}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and y is 6y. Multiply \frac{1}{6} times \frac{y}{y}. Multiply \frac{1}{y} times \frac{6}{6}.

$$\frac{6-y}{6\left(\frac{y}{6y}-\frac{6}{6y}\right)}$$

Since \frac{y}{6y} and \frac{6}{6y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-y}{6\times \frac{y-6}{6y}}$$

Express 6\times \frac{y-6}{6y} as a single fraction.

$$\frac{6-y}{\frac{6\left(y-6\right)}{6y}}$$

Cancel out 6 in both numerator and denominator.

$$\frac{6-y}{\frac{y-6}{y}}$$

Divide 6-y by \frac{y-6}{y} by multiplying 6-y by the reciprocal of \frac{y-6}{y}.

$$\frac{\left(6-y\right)y}{y-6}$$

Extract the negative sign in 6-y.

$$\frac{-y\left(y-6\right)}{y-6}$$

Cancel out y-6 in both numerator and denominator.

$$-y$$

Expand

$$-y$$

Solution Steps

Express \frac{\frac{6-y}{6}}{\frac{1}{6}-\frac{1}{y}} as a single fraction.

$$\frac{6-y}{6\left(\frac{1}{6}-\frac{1}{y}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and y is 6y. Multiply \frac{1}{6} times \frac{y}{y}. Multiply \frac{1}{y} times \frac{6}{6}.

$$\frac{6-y}{6\left(\frac{y}{6y}-\frac{6}{6y}\right)}$$

Since \frac{y}{6y} and \frac{6}{6y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-y}{6\times \frac{y-6}{6y}}$$

Express 6\times \frac{y-6}{6y} as a single fraction.

$$\frac{6-y}{\frac{6\left(y-6\right)}{6y}}$$

Cancel out 6 in both numerator and denominator.

$$\frac{6-y}{\frac{y-6}{y}}$$

Divide 6-y by \frac{y-6}{y} by multiplying 6-y by the reciprocal of \frac{y-6}{y}.

$$\frac{\left(6-y\right)y}{y-6}$$

Extract the negative sign in 6-y.

$$\frac{-y\left(y-6\right)}{y-6}$$

Cancel out y-6 in both numerator and denominator.

$$-y$$