Solve 5/6ab-2/3ac+3/4abc

$$\frac { 5 } { 6 a b } - \frac { 2 } { 3 a c } + \frac { 3 } { 4 a b c }$$

Evaluate

$$\frac{9+10c-8b}{12abc}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6ab and 3ac is 6abc. Multiply \frac{5}{6ab} times \frac{c}{c}. Multiply \frac{2}{3ac} times \frac{2b}{2b}.

$$\frac{5c}{6abc}-\frac{2\times 2b}{6abc}+\frac{3}{4abc}$$

Since \frac{5c}{6abc} and \frac{2\times 2b}{6abc} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5c-2\times 2b}{6abc}+\frac{3}{4abc}$$

Do the multiplications in 5c-2\times 2b.

$$\frac{5c-4b}{6abc}+\frac{3}{4abc}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6abc and 4abc is 12abc. Multiply \frac{5c-4b}{6abc} times \frac{2}{2}. Multiply \frac{3}{4abc} times \frac{3}{3}.

$$\frac{2\left(5c-4b\right)}{12abc}+\frac{3\times 3}{12abc}$$

Since \frac{2\left(5c-4b\right)}{12abc} and \frac{3\times 3}{12abc} have the same denominator, add them by adding their numerators.

$$\frac{2\left(5c-4b\right)+3\times 3}{12abc}$$

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

$$\frac{10c-8b+9}{12abc}$$

Factor

$$\frac{9+10c-8b}{12abc}$$