Solve 5/(B-A)6+2/(B-A)9

$$\frac { 5 } { ( B - A ) 6 } + \frac { 2 } { ( B - A ) 9 }$$

Evaluate

$$\frac{19}{18\left(B-A\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(B-A\right)\times 6 and \left(B-A\right)\times 9 is 18\left(-A+B\right). Multiply \frac{5}{\left(B-A\right)\times 6} times \frac{3}{3}. Multiply \frac{2}{\left(B-A\right)\times 9} times \frac{2}{2}.

$$\frac{5\times 3}{18\left(-A+B\right)}+\frac{2\times 2}{18\left(-A+B\right)}$$

Since \frac{5\times 3}{18\left(-A+B\right)} and \frac{2\times 2}{18\left(-A+B\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\times 3+2\times 2}{18\left(-A+B\right)}$$

Do the multiplications in 5\times 3+2\times 2.

$$\frac{15+4}{18\left(-A+B\right)}$$

Do the calculations in 15+4.

$$\frac{19}{18\left(-A+B\right)}$$

Expand 18\left(-A+B\right).

$$\frac{19}{-18A+18B}$$

Expand

$$\frac{19}{18\left(B-A\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(B-A\right)\times 6 and \left(B-A\right)\times 9 is 18\left(-A+B\right). Multiply \frac{5}{\left(B-A\right)\times 6} times \frac{3}{3}. Multiply \frac{2}{\left(B-A\right)\times 9} times \frac{2}{2}.

$$\frac{5\times 3}{18\left(-A+B\right)}+\frac{2\times 2}{18\left(-A+B\right)}$$

Since \frac{5\times 3}{18\left(-A+B\right)} and \frac{2\times 2}{18\left(-A+B\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\times 3+2\times 2}{18\left(-A+B\right)}$$

Do the multiplications in 5\times 3+2\times 2.

$$\frac{15+4}{18\left(-A+B\right)}$$

Do the calculations in 15+4.

$$\frac{19}{18\left(-A+B\right)}$$

Expand 18\left(-A+B\right).

$$\frac{19}{-18A+18B}$$