What is the answer to x/((1-x))=2.5 ?

The answer to x/((1-x))=2.5 is x= 5/7

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x/((1-x))=2.5

\frac{x}{( 1 - x )} = 2.5

x = \frac{5}{7}

Solution steps

\frac{x}{( 1 - x )} = 2.5

Simplify

\frac{x}{( 1 - x )} : \frac{x}{1 - x}

\frac{x}{1 - x} = 2.5

Multiply both sides by

1 - x

x = 2.5 (1 - x)

Multiply both sides by

10

x \cdot 10 = 25 (1 - x)

Expand

25 (1 - x) : 25 - 25 x

x \cdot 10 = 25 - 25 x

Move

25 x

to the left side

35 x = 25

Divide both sides by

35

x = \frac{5}{7}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = \frac{5}{7}

24 = \frac{6}{x ^{4}} \cdot x^{2}

\frac{4 x + 3}{4 x - 7} = \frac{5}{3}

x \frac{3}{x} + 5 = 0

0 = \frac{x ^{2} - 4}{x - 2}

10 - \frac{19}{x} = 4 + \frac{5}{x}