What is the answer to ((k-1)^6-1)/(3k)=7 ?

The answer to ((k-1)^6-1)/(3k)=7 is k=3

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((k-1)^6-1)/(3k)=7

\frac{( k - 1 ) ^{6} - 1}{3 k} = 7

k = 3

Solution steps

\frac{( k - 1 ) ^{6} - 1}{3 k} = 7

Simplify

\frac{( k - 1 ) ^{6} - 1}{3 k} : \frac{( k - 2 ) ( k ^{4} - 4 k ^{3} + 7 k ^{2} - 6 k + 3 )}{3}

\frac{( k - 2 ) ( k ^{4} - 4 k ^{3} + 7 k ^{2} - 6 k + 3 )}{3} = 7

Multiply both sides by

3

(k - 2) (k^{4} - 4 k^{3} + 7 k^{2} - 6 k + 3) = 21

Solve

(k - 2) (k^{4} - 4 k^{3} + 7 k^{2} - 6 k + 3) = 21 : k = 3

k = 3

Verify Solutions

Find undefined (singularity) points:

k = 0

Combine undefined points with solutions:

k = 3

t, s = \frac{d}{t - t o}

\frac{1}{x - 1} + \frac{2 x}{x - 1} = 5

\frac{8 - 4 x}{x - 2} = x

\frac{2 k}{k - 1} = \frac{21 - k}{2 k}

49 = \frac{( 3 x + 8 ) ^{2}}{x ^{2}}

What is the answer to ((k-1)^6-1)/(3k)=7 ?
The answer to ((k-1)^6-1)/(3k)=7 is k=3
Solve for k: ((k-1)^6-1)/(3k)=7
The solution is k=3