What is the answer to (x-4)/(x-9)=9 ?

The answer to (x-4)/(x-9)=9 is x= 77/8

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(x-4)/(x-9)=9

\frac{x - 4}{x - 9} = 9

x = \frac{77}{8}

Decimal Notation

x = 9.625

Solution steps

\frac{x - 4}{x - 9} = 9

Multiply both sides by

x - 9

x - 4 = 9 (x - 9)

Expand

9 (x - 9) : 9 x - 81

x - 4 = 9 x - 81

Move

4

to the right side

x = 9 x - 77

Move

9 x

to the left side

- 8 x = - 77

Divide both sides by

- 8

x = \frac{77}{8}

Verify Solutions

Find undefined (singularity) points:

x = 9

Combine undefined points with solutions:

x = \frac{77}{8}

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

- \frac{72}{x ^{2}} + 2 = 0

\frac{3}{2} = \frac{4}{a}

7 + \frac{8}{x} = 5

\frac{x ^{2} - 9}{x + 2} = 8