What is the answer to (x-4)/(x-1)=(12)/(3-x)+1 ?

The answer to (x-4)/(x-1)=(12)/(3-x)+1 is x= 1/3

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(x-4)/(x-1)=(12)/(3-x)+1

\frac{x - 4}{x - 1} = \frac{12}{3 - x} + 1

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

\frac{x - 4}{x - 1} = \frac{12}{3 - x} + 1

Multiply by LCM

- x^{2} + 7 x - 12 = - x^{2} + 16 x - 15

Move

12

to the right side

- x^{2} + 7 x = - x^{2} + 16 x - 3

Subtract

- x^{2} + 16 x

from both sides

- x^{2} + 7 x - (- x^{2} + 16 x) = - x^{2} + 16 x - 3 - (- x^{2} + 16 x)

Simplify

- 9 x = - 3

Divide both sides by

- 9

x = \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 3

Combine undefined points with solutions:

x = \frac{1}{3}

0 = 2 x - \frac{128}{x ^{2}}

\frac{x ^{2} + 5 x + 6}{x + 3} = 0

\frac{8}{32} = \frac{2}{x}

14 = \frac{56}{x}

\frac{x + 6}{x + 3} = 2 - \frac{5 x + 12}{x + 3}

What is the answer to (x-4)/(x-1)=(12)/(3-x)+1 ?
The answer to (x-4)/(x-1)=(12)/(3-x)+1 is x= 1/3
Solve for x: (x-4)/(x-1)=(12)/(3-x)+1
The solution is x= 1/3