Solve 2/y-3-7y-14/y^2-5y+6

$$\frac { 2 } { y - 3 } - \frac { 7 y - 14 } { y ^ { 2 } - 5 y + 6 }$$

Evaluate

$$-\frac{5}{y-3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{7y-14}{y^{2}-5y+6}.

$$\frac{2}{y-3}-\frac{7\left(y-2\right)}{\left(y-3\right)\left(y-2\right)}$$

Cancel out y-2 in both numerator and denominator.

$$\frac{2}{y-3}-\frac{7}{y-3}$$

Since \frac{2}{y-3} and \frac{7}{y-3} have the same denominator, subtract them by subtracting their numerators. Subtract 7 from 2 to get -5.

$$\frac{-5}{y-3}$$

Expand

$$-\frac{5}{y-3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{7y-14}{y^{2}-5y+6}.

$$\frac{2}{y-3}-\frac{7\left(y-2\right)}{\left(y-3\right)\left(y-2\right)}$$

Cancel out y-2 in both numerator and denominator.

$$\frac{2}{y-3}-\frac{7}{y-3}$$

Since \frac{2}{y-3} and \frac{7}{y-3} have the same denominator, subtract them by subtracting their numerators. Subtract 7 from 2 to get -5.

$$\frac{-5}{y-3}$$