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

The answer to (2x+3)/(1-x)=4 is x= 1/6

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

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

x = \frac{1}{6}

Decimal Notation

x = 0.16666 \dots

Solution steps

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

Multiply both sides by

1 - x

2 x + 3 = 4 (1 - x)

Expand

4 (1 - x) : 4 - 4 x

2 x + 3 = 4 - 4 x

Move

3

to the right side

2 x = - 4 x + 1

Move

4 x

to the left side

6 x = 1

Divide both sides by

6

x = \frac{1}{6}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = \frac{1}{6}

8 x^{- 3} = 64

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

103 = \frac{2 x - 3}{10 - 6 x}

\frac{1}{x + 1} + 2 = \frac{7}{x + 1}

\frac{3 x}{x ^{2} - 7 x} = 8