What is the answer to 3/(k+1)=(12)/(k-12) ?

The answer to 3/(k+1)=(12)/(k-12) is k=-16/3

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3/(k+1)=(12)/(k-12)

\frac{3}{k + 1} = \frac{12}{k - 12}

k = - \frac{16}{3}

Decimal Notation

k = - 5.33333 \dots

Solution steps

\frac{3}{k + 1} = \frac{12}{k - 12}

Cross multiply

3 k - 36 = 12 k + 12

Move

36

to the right side

3 k = 12 k + 48

Move

12 k

to the left side

- 9 k = 48

Divide both sides by

- 9

k = - \frac{16}{3}

Verify Solutions

Find undefined (singularity) points:

k = - 1, k = 12

Combine undefined points with solutions:

k = - \frac{16}{3}

\frac{x ^{2} + 1}{x ^{2} - 1} = 0

\frac{- 20}{x + 5} = \frac{- 10}{x}

x, \frac{a x + b}{c x + d} = 3

x, \frac{a x + b}{c x + d} = 9

\frac{x ^{2} - 2 x - 1}{( x - 1 ) ^{2}} = 0

What is the answer to 3/(k+1)=(12)/(k-12) ?
The answer to 3/(k+1)=(12)/(k-12) is k=-16/3
Solve for k: 3/(k+1)=(12)/(k-12)
The solution is k=-16/3