Solve 2*1/k*1/k*4/2+4k^2

$$\frac { 2 \times \frac { 1 } { k } \times \frac { 1 } { k } \times 4 } { 2 + 4 k ^ { 2 } }$$

Evaluate

$$\frac{4}{k^{2}\left(2k^{2}+1\right)}$$

Solution Steps

Multiply \frac{1}{k} and \frac{1}{k} to get \left(\frac{1}{k}\right)^{2}.

$$\frac{2\times \left(\frac{1}{k}\right)^{2}\times 4}{2+4k^{2}}$$

To raise \frac{1}{k} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{2\times \frac{1^{2}}{k^{2}}\times 4}{2+4k^{2}}$$

Multiply 2 and 4 to get 8.

$$\frac{8\times \frac{1^{2}}{k^{2}}}{2+4k^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{8\times \frac{1}{k^{2}}}{2+4k^{2}}$$

Express 8\times \frac{1}{k^{2}} as a single fraction.

$$\frac{\frac{8}{k^{2}}}{2+4k^{2}}$$

Express \frac{\frac{8}{k^{2}}}{2+4k^{2}} as a single fraction.

$$\frac{8}{k^{2}\left(2+4k^{2}\right)}$$

Use the distributive property to multiply k^{2} by 2+4k^{2}.

$$\frac{8}{2k^{2}+4k^{4}}$$

Factor

$$\frac{4}{k^{2}\left(2k^{2}+1\right)}$$