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

The answer to x/(3^2-x)=2^2 is x= 36/5

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x/(3^2-x)=2^2

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

x = \frac{36}{5}

Decimal Notation

x = 7.2

Solution steps

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

Simplify

\frac{x}{3 ^{2} - x} : \frac{x}{9 - x}

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

Multiply both sides by

9 - x

x = 4 (9 - x)

Expand

4 (9 - x) : 36 - 4 x

x = 36 - 4 x

Move

4 x

to the left side

5 x = 36

Divide both sides by

5

x = \frac{36}{5}

Verify Solutions

Find undefined (singularity) points:

x = 9

Combine undefined points with solutions:

x = \frac{36}{5}

4 + \frac{6}{y - 3} = \frac{2 y}{y - 3}

\frac{10}{h} = \frac{52}{13}

\frac{18 x}{( x ^{2} + 3 ) ^{2}} = 0

\frac{6}{x - 5} = \frac{4}{x}

\frac{x ^{2} + x - 6}{x + 1} = 0