What is the answer to (x-6)/(4-x)=3 ?

The answer to (x-6)/(4-x)=3 is x= 9/2

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(x-6)/(4-x)=3

\frac{x - 6}{4 - x} = 3

x = \frac{9}{2}

Decimal Notation

x = 4.5

Solution steps

\frac{x - 6}{4 - x} = 3

Multiply both sides by

4 - x

x - 6 = 3 (4 - x)

Expand

3 (4 - x) : 12 - 3 x

x - 6 = 12 - 3 x

Move

6

to the right side

x = - 3 x + 18

Move

3 x

to the left side

4 x = 18

Divide both sides by

4

x = \frac{9}{2}

Verify Solutions

Find undefined (singularity) points:

x = 4

Combine undefined points with solutions:

x = \frac{9}{2}

\frac{6 t + 4}{3 t} = \frac{2 t + 5}{t}

f, f^{- 1} (x) = x^{4} + 2

7 = \frac{6}{x} + 5

s, n = \frac{L}{p ( r + s )}

20 + 10 [\frac{2}{2 + m}] = 22.2