Solve w/8-1/2/frac{3{8w}+3/4}

$$\frac { \frac { w } { 8 } - \frac { 1 } { 2 } } { \frac { 3 } { 8 w } + \frac { 3 } { 4 } }$$

Evaluate

$$\frac{w\left(w-4\right)}{3\left(2w+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 2 is 8. Multiply \frac{1}{2} times \frac{4}{4}.

$$\frac{\frac{w}{8}-\frac{4}{8}}{\frac{3}{8w}+\frac{3}{4}}$$

Since \frac{w}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{w-4}{8}}{\frac{3}{8w}+\frac{3}{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8w and 4 is 8w. Multiply \frac{3}{4} times \frac{2w}{2w}.

$$\frac{\frac{w-4}{8}}{\frac{3}{8w}+\frac{3\times 2w}{8w}}$$

Since \frac{3}{8w} and \frac{3\times 2w}{8w} have the same denominator, add them by adding their numerators.

$$\frac{\frac{w-4}{8}}{\frac{3+3\times 2w}{8w}}$$

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

$$\frac{\frac{w-4}{8}}{\frac{3+6w}{8w}}$$

Divide \frac{w-4}{8} by \frac{3+6w}{8w} by multiplying \frac{w-4}{8} by the reciprocal of \frac{3+6w}{8w}.

$$\frac{\left(w-4\right)\times 8w}{8\left(3+6w\right)}$$

Cancel out 8 in both numerator and denominator.

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

Use the distributive property to multiply w by w-4.

$$\frac{w^{2}-4w}{6w+3}$$

Expand

$$\frac{w^{2}-4w}{3\left(2w+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 2 is 8. Multiply \frac{1}{2} times \frac{4}{4}.

$$\frac{\frac{w}{8}-\frac{4}{8}}{\frac{3}{8w}+\frac{3}{4}}$$

Since \frac{w}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{w-4}{8}}{\frac{3}{8w}+\frac{3}{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8w and 4 is 8w. Multiply \frac{3}{4} times \frac{2w}{2w}.

$$\frac{\frac{w-4}{8}}{\frac{3}{8w}+\frac{3\times 2w}{8w}}$$

Since \frac{3}{8w} and \frac{3\times 2w}{8w} have the same denominator, add them by adding their numerators.

$$\frac{\frac{w-4}{8}}{\frac{3+3\times 2w}{8w}}$$

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

$$\frac{\frac{w-4}{8}}{\frac{3+6w}{8w}}$$

Divide \frac{w-4}{8} by \frac{3+6w}{8w} by multiplying \frac{w-4}{8} by the reciprocal of \frac{3+6w}{8w}.

$$\frac{\left(w-4\right)\times 8w}{8\left(3+6w\right)}$$

Cancel out 8 in both numerator and denominator.

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

Use the distributive property to multiply w by w-4.

$$\frac{w^{2}-4w}{6w+3}$$