What is the answer to 1/(x-2)-3= 4/(2-x) ?

The answer to 1/(x-2)-3= 4/(2-x) is x= 11/3

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1/(x-2)-3= 4/(2-x)

\frac{1}{x - 2} - 3 = \frac{4}{2 - x}

x = \frac{11}{3}

Decimal Notation

x = 3.66666 \dots

Solution steps

\frac{1}{x - 2} - 3 = \frac{4}{2 - x}

Multiply by LCM

- x + 2 - 3 (x - 2) (- x + 2) = 4 (x - 2)

Solve

- x + 2 - 3 (x - 2) (- x + 2) = 4 (x - 2) : x = \frac{11}{3}, x = 2

x = \frac{11}{3}, x = 2

Verify Solutions

Find undefined (singularity) points:

x = 2

Since the equation is undefined for:

2

x = \frac{11}{3}

x, y = \frac{y}{x}

\frac{x + 3}{x + 4} = 0

\frac{6}{x - 2} - \frac{4}{x + 2} = 1

a = \frac{( 12 ( 0 ) ^{2} + 6 ) m}{s ^{2}}

\frac{- 2}{x} = \frac{3}{5}

What is the answer to 1/(x-2)-3= 4/(2-x) ?
The answer to 1/(x-2)-3= 4/(2-x) is x= 11/3
Solve for x: 1/(x-2)-3= 4/(2-x)
The solution is x= 11/3