Solve y-6/5y-15[1+y/y-6]

$$\frac { y - 6 } { 5 y - 15 } [ 1 + \frac { y } { y - 6 } ]$$

Evaluate

$$\frac{2}{5}=0.4$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y-6}{y-6}.

$$\frac{y-6}{5y-15}\left(\frac{y-6}{y-6}+\frac{y}{y-6}\right)$$

Since \frac{y-6}{y-6} and \frac{y}{y-6} have the same denominator, add them by adding their numerators.

$$\frac{y-6}{5y-15}\times \frac{y-6+y}{y-6}$$

Combine like terms in y-6+y.

$$\frac{y-6}{5y-15}\times \frac{2y-6}{y-6}$$

Multiply \frac{y-6}{5y-15} times \frac{2y-6}{y-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y-6\right)\left(2y-6\right)}{\left(5y-15\right)\left(y-6\right)}$$

Cancel out y-6 in both numerator and denominator.

$$\frac{2y-6}{5y-15}$$

Factor the expressions that are not already factored.

$$\frac{2\left(y-3\right)}{5\left(y-3\right)}$$

Cancel out y-3 in both numerator and denominator.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$