Solve 1/6k^2=1/3k^2-1/k

Evaluate

\frac{1}{6} k^{2} = \frac{1}{3} k^{2} - \frac{1}{k}

Find the domain

\frac{1}{6} k^{2} = \frac{1}{3} k^{2} - \frac{1}{k}, k \neq = 0

Multiply both sides of the equation by LCD

\frac{1}{6} k^{2} \times 6 k = (\frac{1}{3} k^{2} - \frac{1}{k}) \times 6 k

Simplify the equation

More Steps

k^{3} = (\frac{1}{3} k^{2} - \frac{1}{k}) \times 6 k

Simplify the equation

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k^{3} = 2 k^{3} - 6

Move the expression to the left side

k^{3} - (2 k^{3} - 6) = 0

Subtract the terms

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- k^{3} + 6 = 0

Move the constant to the right-hand side and change its sign

- k^{3} = 0 - 6

Removing 0 doesn't change the value,so remove it from the expression

- k^{3} = - 6

Change the signs on both sides of the equation

k^{3} = 6

Take the 3 -th root on both sides of the equation

3 k^{3} = 36

Calculate

k = 36

Check if the solution is in the defined range

k = 36, k \neq = 0

Solution

k = 36

Alternative Form

k \approx 1.817121

Solve the equation