Solve -k(20/k)^2/2+20*20/k

$$- k \frac { ( \frac { 20 } { k } ) ^ { 2 } } { 2 } + 20 \times \frac { 20 } { k }$$

Evaluate

$$\frac{200}{k}$$

Short Solution Steps

To raise \frac{20}{k} to a power, raise both numerator and denominator to the power and then divide.

$$\left(-k\right)\times \frac{\frac{20^{2}}{k^{2}}}{2}+20\times \frac{20}{k}$$

Express \frac{\frac{20^{2}}{k^{2}}}{2} as a single fraction.

$$\left(-k\right)\times \frac{20^{2}}{k^{2}\times 2}+20\times \frac{20}{k}$$

Calculate 20 to the power of 2 and get 400.

$$\left(-k\right)\times \frac{400}{k^{2}\times 2}+20\times \frac{20}{k}$$

Express \left(-k\right)\times \frac{400}{k^{2}\times 2} as a single fraction.

$$\frac{-k\times 400}{k^{2}\times 2}+20\times \frac{20}{k}$$

Cancel out 2k in both numerator and denominator.

$$\frac{-200}{k}+20\times \frac{20}{k}$$

Express 20\times \frac{20}{k} as a single fraction.

$$\frac{-200}{k}+\frac{20\times 20}{k}$$

Since \frac{-200}{k} and \frac{20\times 20}{k} have the same denominator, add them by adding their numerators.

$$\frac{-200+20\times 20}{k}$$

Do the multiplications in -200+20\times 20.

$$\frac{-200+400}{k}$$

Do the calculations in -200+400.

$$\frac{200}{k}$$

Expand

$$\frac{200}{k}$$

Short Solution Steps

To raise \frac{20}{k} to a power, raise both numerator and denominator to the power and then divide.

$$\left(-k\right)\times \frac{\frac{20^{2}}{k^{2}}}{2}+20\times \frac{20}{k}$$

Express \frac{\frac{20^{2}}{k^{2}}}{2} as a single fraction.

$$\left(-k\right)\times \frac{20^{2}}{k^{2}\times 2}+20\times \frac{20}{k}$$

Calculate 20 to the power of 2 and get 400.

$$\left(-k\right)\times \frac{400}{k^{2}\times 2}+20\times \frac{20}{k}$$

Express \left(-k\right)\times \frac{400}{k^{2}\times 2} as a single fraction.

$$\frac{-k\times 400}{k^{2}\times 2}+20\times \frac{20}{k}$$

Cancel out 2k in both numerator and denominator.

$$\frac{-200}{k}+20\times \frac{20}{k}$$

Express 20\times \frac{20}{k} as a single fraction.

$$\frac{-200}{k}+\frac{20\times 20}{k}$$

Since \frac{-200}{k} and \frac{20\times 20}{k} have the same denominator, add them by adding their numerators.

$$\frac{-200+20\times 20}{k}$$

Do the multiplications in -200+20\times 20.

$$\frac{-200+400}{k}$$

Do the calculations in -200+400.

$$\frac{200}{k}$$