Solve 5/2(e-f)+4/3(f-e)

$$\frac { 5 } { 2 ( e - f ) } + \frac { 4 } { 3 ( f - e ) }$$

Evaluate

$$\frac{7}{6\left(e-f\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(e-f\right) and 3\left(f-e\right) is 6\left(-f+e\right). Multiply \frac{5}{2\left(e-f\right)} times \frac{3}{3}. Multiply \frac{4}{3\left(f-e\right)} times \frac{-2}{-2}.

$$\frac{5\times 3}{6\left(-f+e\right)}+\frac{4\left(-2\right)}{6\left(-f+e\right)}$$

Since \frac{5\times 3}{6\left(-f+e\right)} and \frac{4\left(-2\right)}{6\left(-f+e\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\times 3+4\left(-2\right)}{6\left(-f+e\right)}$$

Do the multiplications in 5\times 3+4\left(-2\right).

$$\frac{15-8}{6\left(-f+e\right)}$$

Do the calculations in 15-8.

$$\frac{7}{6\left(-f+e\right)}$$

Expand 6\left(-f+e\right).

$$\frac{7}{-6f+6e}$$

Expand

$$\frac{7}{6\left(e-f\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(e-f\right) and 3\left(f-e\right) is 6\left(-f+e\right). Multiply \frac{5}{2\left(e-f\right)} times \frac{3}{3}. Multiply \frac{4}{3\left(f-e\right)} times \frac{-2}{-2}.

$$\frac{5\times 3}{6\left(-f+e\right)}+\frac{4\left(-2\right)}{6\left(-f+e\right)}$$

Since \frac{5\times 3}{6\left(-f+e\right)} and \frac{4\left(-2\right)}{6\left(-f+e\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\times 3+4\left(-2\right)}{6\left(-f+e\right)}$$

Do the multiplications in 5\times 3+4\left(-2\right).

$$\frac{15-8}{6\left(-f+e\right)}$$

Do the calculations in 15-8.

$$\frac{7}{6\left(-f+e\right)}$$

Expand 6\left(-f+e\right).

$$\frac{7}{-6f+6e}$$