Solve (1/7-y)(1/y-y)

$$( \frac { 1 } { 7 } - y ) ( \frac { 1 } { y } - y )$$

Evaluate

$$y^{2}-\frac{y}{7}-1+\frac{1}{7y}$$

Short Solution Steps

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

$$\left(\frac{1}{7}-y\right)\left(\frac{1}{y}-\frac{yy}{y}\right)$$

Since \frac{1}{y} and \frac{yy}{y} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{1}{7}-y\right)\times \frac{1-yy}{y}$$

Do the multiplications in 1-yy.

$$\left(\frac{1}{7}-y\right)\times \frac{1-y^{2}}{y}$$

Use the distributive property to multiply \frac{1}{7}-y by \frac{1-y^{2}}{y}.

$$\frac{1}{7}\times \frac{1-y^{2}}{y}-y\times \frac{1-y^{2}}{y}$$

Multiply \frac{1}{7} times \frac{1-y^{2}}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1-y^{2}}{7y}-y\times \frac{1-y^{2}}{y}$$

Cancel out y and y.

$$\frac{1-y^{2}}{7y}-\left(1-y^{2}\right)$$

To find the opposite of 1-y^{2}, find the opposite of each term.

$$\frac{1-y^{2}}{7y}-1-\left(-y^{2}\right)$$

The opposite of -y^{2} is y^{2}.

$$\frac{1-y^{2}}{7y}-1+y^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -1+y^{2} times \frac{7y}{7y}.

$$\frac{1-y^{2}}{7y}+\frac{\left(-1+y^{2}\right)\times 7y}{7y}$$

Since \frac{1-y^{2}}{7y} and \frac{\left(-1+y^{2}\right)\times 7y}{7y} have the same denominator, add them by adding their numerators.

$$\frac{1-y^{2}+\left(-1+y^{2}\right)\times 7y}{7y}$$

Do the multiplications in 1-y^{2}+\left(-1+y^{2}\right)\times 7y.

$$\frac{1-y^{2}-7y+7y^{3}}{7y}$$

Expand

$$y^{2}-\frac{y}{7}-1+\frac{1}{7y}$$

Short Solution Steps

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

$$\left(\frac{1}{7}-y\right)\left(\frac{1}{y}-\frac{yy}{y}\right)$$

Since \frac{1}{y} and \frac{yy}{y} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{1}{7}-y\right)\times \frac{1-yy}{y}$$

Do the multiplications in 1-yy.

$$\left(\frac{1}{7}-y\right)\times \frac{1-y^{2}}{y}$$

Use the distributive property to multiply \frac{1}{7}-y by \frac{1-y^{2}}{y}.

$$\frac{1}{7}\times \frac{1-y^{2}}{y}-y\times \frac{1-y^{2}}{y}$$

Multiply \frac{1}{7} times \frac{1-y^{2}}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1-y^{2}}{7y}-y\times \frac{1-y^{2}}{y}$$

Cancel out y and y.

$$\frac{1-y^{2}}{7y}-\left(1-y^{2}\right)$$

To find the opposite of 1-y^{2}, find the opposite of each term.

$$\frac{1-y^{2}}{7y}-1-\left(-y^{2}\right)$$

The opposite of -y^{2} is y^{2}.

$$\frac{1-y^{2}}{7y}-1+y^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -1+y^{2} times \frac{7y}{7y}.

$$\frac{1-y^{2}}{7y}+\frac{\left(-1+y^{2}\right)\times 7y}{7y}$$

Since \frac{1-y^{2}}{7y} and \frac{\left(-1+y^{2}\right)\times 7y}{7y} have the same denominator, add them by adding their numerators.

$$\frac{1-y^{2}+\left(-1+y^{2}\right)\times 7y}{7y}$$

Do the multiplications in 1-y^{2}+\left(-1+y^{2}\right)\times 7y.

$$\frac{1-y^{2}-7y+7y^{3}}{7y}$$