Solve 4f/10f-5d+2d/6f-3d

$$\frac { 4 f } { 10 f - 5 d } + \frac { 2 d } { 6 f - 3 d }$$

Evaluate

$$\frac{2\left(5d+6f\right)}{15\left(2f-d\right)}$$

Short Solution Steps

Factor 10f-5d. Factor 6f-3d.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(-d+2f\right) and 3\left(-d+2f\right) is 15\left(-d+2f\right). Multiply \frac{4f}{5\left(-d+2f\right)} times \frac{3}{3}. Multiply \frac{2d}{3\left(-d+2f\right)} times \frac{5}{5}.

$$\frac{3\times 4f}{15\left(-d+2f\right)}+\frac{5\times 2d}{15\left(-d+2f\right)}$$

Since \frac{3\times 4f}{15\left(-d+2f\right)} and \frac{5\times 2d}{15\left(-d+2f\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\times 4f+5\times 2d}{15\left(-d+2f\right)}$$

Do the multiplications in 3\times 4f+5\times 2d.

$$\frac{12f+10d}{15\left(-d+2f\right)}$$

Expand 15\left(-d+2f\right).

$$\frac{12f+10d}{-15d+30f}$$

Factor

$$\frac{2\left(5d+6f\right)}{15\left(2f-d\right)}$$