Solve x-1/6-8a/2b+a/3b

$$\frac { x - 1 } { 6 } - \frac { 8 a } { 2 b } + \frac { a } { 3 b }$$

Evaluate

$$\frac{x}{6}-\frac{11a}{3b}-\frac{1}{6}$$

Short Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{x-1}{6}-\frac{4a}{b}+\frac{a}{3b}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and b is 6b. Multiply \frac{x-1}{6} times \frac{b}{b}. Multiply \frac{4a}{b} times \frac{6}{6}.

$$\frac{\left(x-1\right)b}{6b}-\frac{6\times 4a}{6b}+\frac{a}{3b}$$

Since \frac{\left(x-1\right)b}{6b} and \frac{6\times 4a}{6b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-1\right)b-6\times 4a}{6b}+\frac{a}{3b}$$

Do the multiplications in \left(x-1\right)b-6\times 4a.

$$\frac{xb-b-24a}{6b}+\frac{a}{3b}$$

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

$$\frac{xb-b-24a}{6b}+\frac{2a}{6b}$$

Since \frac{xb-b-24a}{6b} and \frac{2a}{6b} have the same denominator, add them by adding their numerators.

$$\frac{xb-b-24a+2a}{6b}$$

Combine like terms in xb-b-24a+2a.

$$\frac{xb-b-22a}{6b}$$

Expand

$$\frac{x}{6}-\frac{11a}{3b}-\frac{1}{6}$$

Short Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{x-1}{6}-\frac{4a}{b}+\frac{a}{3b}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and b is 6b. Multiply \frac{x-1}{6} times \frac{b}{b}. Multiply \frac{4a}{b} times \frac{6}{6}.

$$\frac{\left(x-1\right)b}{6b}-\frac{6\times 4a}{6b}+\frac{a}{3b}$$

Since \frac{\left(x-1\right)b}{6b} and \frac{6\times 4a}{6b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-1\right)b-6\times 4a}{6b}+\frac{a}{3b}$$

Do the multiplications in \left(x-1\right)b-6\times 4a.

$$\frac{xb-b-24a}{6b}+\frac{a}{3b}$$

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

$$\frac{xb-b-24a}{6b}+\frac{2a}{6b}$$

Since \frac{xb-b-24a}{6b} and \frac{2a}{6b} have the same denominator, add them by adding their numerators.

$$\frac{xb-b-24a+2a}{6b}$$

Combine like terms in xb-b-24a+2a.

$$\frac{xb-b-22a}{6b}$$