Solve 12/-9+2/3-m

$$\frac { 12 } { - 9 } + \frac { 2 } { 3 - m }$$

Evaluate

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

Short Solution Steps

Reduce the fraction \frac{12}{-9} to lowest terms by extracting and canceling out 3.

$$-\frac{4}{3}+\frac{2}{3-m}$$

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

$$-\frac{4\left(-m+3\right)}{3\left(-m+3\right)}+\frac{2\times 3}{3\left(-m+3\right)}$$

Since -\frac{4\left(-m+3\right)}{3\left(-m+3\right)} and \frac{2\times 3}{3\left(-m+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{-4\left(-m+3\right)+2\times 3}{3\left(-m+3\right)}$$

Do the multiplications in -4\left(-m+3\right)+2\times 3.

$$\frac{4m-12+6}{3\left(-m+3\right)}$$

Combine like terms in 4m-12+6.

$$\frac{4m-6}{3\left(-m+3\right)}$$

Expand 3\left(-m+3\right).

$$\frac{4m-6}{-3m+9}$$

Factor

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