Solve 1/y-1/8/frac{y-8{y}}

$$\frac { \frac { 1 } { y } - \frac { 1 } { 8 } } { \frac { y - 8 } { y } }$$

Evaluate

$$-\frac{1}{8}=-0.125$$

Solution Steps

Divide \frac{1}{y}-\frac{1}{8} by \frac{y-8}{y} by multiplying \frac{1}{y}-\frac{1}{8} by the reciprocal of \frac{y-8}{y}.

$$\frac{\left(\frac{1}{y}-\frac{1}{8}\right)y}{y-8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 8 is 8y. Multiply \frac{1}{y} times \frac{8}{8}. Multiply \frac{1}{8} times \frac{y}{y}.

$$\frac{\left(\frac{8}{8y}-\frac{y}{8y}\right)y}{y-8}$$

Since \frac{8}{8y} and \frac{y}{8y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8-y}{8y}y}{y-8}$$

Express \frac{8-y}{8y}y as a single fraction.

$$\frac{\frac{\left(8-y\right)y}{8y}}{y-8}$$

Cancel out y in both numerator and denominator.

$$\frac{\frac{-y+8}{8}}{y-8}$$

Express \frac{\frac{-y+8}{8}}{y-8} as a single fraction.

$$\frac{-y+8}{8\left(y-8\right)}$$

Extract the negative sign in -y+8.

$$\frac{-\left(y-8\right)}{8\left(y-8\right)}$$

Cancel out y-8 in both numerator and denominator.

$$\frac{-1}{8}$$

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$-\frac{1}{8}$$

Factor

$$-\frac{1}{8} = -0.125$$