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

The answer to 3/(x-2)=4-1/3 is x= 31/11

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

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

x = \frac{31}{11}

Decimal Notation

x = 2.81818 \dots

Solution steps

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

Multiply by LCM

9 = 11 (x - 2)

Switch sides

11 (x - 2) = 9

Divide both sides by

11

x - 2 = \frac{9}{11}

Move

2

to the right side

x = \frac{31}{11}

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = \frac{31}{11}

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

\frac{36}{4 x - 3} = 4

3 x^{- 2} - 14 x^{- 1} - 5 = 0

n (x) = \frac{( 7 x + 5 )}{( x - 8 )}

\frac{x + 1}{3 x} = \frac{1}{6}