Solve y-1/3y-12-y-3/2y-8

$$\frac { y - 1 } { 3 y - 12 } - \frac { y - 3 } { 2 y - 8 }$$

Evaluate

$$\frac{7-y}{6\left(y-4\right)}$$

Short Solution Steps

Factor 3y-12. Factor 2y-8.

$$\frac{y-1}{3\left(y-4\right)}-\frac{y-3}{2\left(y-4\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(y-4\right) and 2\left(y-4\right) is 6\left(y-4\right). Multiply \frac{y-1}{3\left(y-4\right)} times \frac{2}{2}. Multiply \frac{y-3}{2\left(y-4\right)} times \frac{3}{3}.

$$\frac{2\left(y-1\right)}{6\left(y-4\right)}-\frac{3\left(y-3\right)}{6\left(y-4\right)}$$

Since \frac{2\left(y-1\right)}{6\left(y-4\right)} and \frac{3\left(y-3\right)}{6\left(y-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(y-1\right)-3\left(y-3\right)}{6\left(y-4\right)}$$

Do the multiplications in 2\left(y-1\right)-3\left(y-3\right).

$$\frac{2y-2-3y+9}{6\left(y-4\right)}$$

Combine like terms in 2y-2-3y+9.

$$\frac{-y+7}{6\left(y-4\right)}$$

Expand 6\left(y-4\right).

$$\frac{-y+7}{6y-24}$$

Expand

$$-\frac{y-7}{6\left(y-4\right)}$$

Short Solution Steps

Factor 3y-12. Factor 2y-8.

$$\frac{y-1}{3\left(y-4\right)}-\frac{y-3}{2\left(y-4\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(y-4\right) and 2\left(y-4\right) is 6\left(y-4\right). Multiply \frac{y-1}{3\left(y-4\right)} times \frac{2}{2}. Multiply \frac{y-3}{2\left(y-4\right)} times \frac{3}{3}.

$$\frac{2\left(y-1\right)}{6\left(y-4\right)}-\frac{3\left(y-3\right)}{6\left(y-4\right)}$$

Since \frac{2\left(y-1\right)}{6\left(y-4\right)} and \frac{3\left(y-3\right)}{6\left(y-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(y-1\right)-3\left(y-3\right)}{6\left(y-4\right)}$$

Do the multiplications in 2\left(y-1\right)-3\left(y-3\right).

$$\frac{2y-2-3y+9}{6\left(y-4\right)}$$

Combine like terms in 2y-2-3y+9.

$$\frac{-y+7}{6\left(y-4\right)}$$

Expand 6\left(y-4\right).

$$\frac{-y+7}{6y-24}$$