Solve 2h/5h-kdiv5k/10h^2-2h

$$\frac { 2 h } { 5 h - k } \div \frac { 5 k } { 10 h ^ { 2 } - 2 h }$$

Evaluate

$$\frac{4\left(5h-1\right)h^{2}}{5k\left(5h-k\right)}$$

Short Solution Steps

Divide \frac{2h}{5h-k} by \frac{5k}{10h^{2}-2h} by multiplying \frac{2h}{5h-k} by the reciprocal of \frac{5k}{10h^{2}-2h}.

$$\frac{2h\left(10h^{2}-2h\right)}{\left(5h-k\right)\times 5k}$$

Use the distributive property to multiply 2h by 10h^{2}-2h.

$$\frac{20h^{3}-4h^{2}}{\left(5h-k\right)\times 5k}$$

Use the distributive property to multiply 5h-k by 5.

$$\frac{20h^{3}-4h^{2}}{\left(25h-5k\right)k}$$

Use the distributive property to multiply 25h-5k by k.

$$\frac{20h^{3}-4h^{2}}{25hk-5k^{2}}$$

Differentiate w.r.t. h

$$\frac{4h\left(50h^{2}-15hk-5h+2k\right)}{5k\left(5h-k\right)^{2}}$$