What is the answer to 1/(2-k)+k+4/7 =1 ?

The answer to 1/(2-k)+k+4/7 =1 is k=-(-17+sqrt(317))/(14),k=(17+sqrt(317))/(14)

Solve for k: 1/(2-k)+k+4/7 =1

The solution is k=-(-17+sqrt(317))/(14),k=(17+sqrt(317))/(14)

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\frac{1}{2 - k} + k + \frac{4}{7} = 1

k = - \frac{- 17 + 317}{14}, k = \frac{17 + 317}{14}

Decimal Notation

k = - 0.05746 \dots, k = 2.48603 \dots

Solution steps

\frac{1}{2 - k} + k + \frac{4}{7} = 1

Multiply by LCM

7 + k \cdot 7 (- k + 2) + 4 (- k + 2) = 7 (- k + 2)

Solve

7 + k \cdot 7 (- k + 2) + 4 (- k + 2) = 7 (- k + 2) : k = - \frac{- 17 + 317}{14}, k = \frac{17 + 317}{14}

k = - \frac{- 17 + 317}{14}, k = \frac{17 + 317}{14}

Verify Solutions

Find undefined (singularity) points:

k = 2

Combine undefined points with solutions:

k = - \frac{- 17 + 317}{14}, k = \frac{17 + 317}{14}

1 - \frac{1}{x} = \frac{12}{x ^{2}}

\frac{x - 5}{x - 1} = - \frac{3}{x}

\frac{x ^{3} - 8 x ^{2}}{8 - x} = 0

\frac{x ^{3} - 8 x ^{2}}{8 - x} = 1

\frac{6}{s + 5} + \frac{s - 5}{2} = 3

What is the answer to 1/(2-k)+k+4/7 =1 ?
The answer to 1/(2-k)+k+4/7 =1 is k=-(-17+sqrt(317))/(14),k=(17+sqrt(317))/(14)
Solve for k: 1/(2-k)+k+4/7 =1
The solution is k=-(-17+sqrt(317))/(14),k=(17+sqrt(317))/(14)