What is the answer to 1/(3-x)=(x^2-9)/((x-3)^2) ?

The answer to 1/(3-x)=(x^2-9)/((x-3)^2) is x=-4

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1/(3-x)=(x^2-9)/((x-3)^2)

\frac{1}{3 - x} = \frac{x ^{2} - 9}{( x - 3 ) ^{2}}

x = - 4

Solution steps

\frac{1}{3 - x} = \frac{x ^{2} - 9}{( x - 3 ) ^{2}}

Cross multiply

x - 3 = (3 - x) (x + 3)

Solve

x - 3 = (3 - x) (x + 3) : x = - 4, x = 3

x = - 4, x = 3

Verify Solutions

Find undefined (singularity) points:

x = 3

Since the equation is undefined for:

3

x = - 4

5 - \frac{900}{x ^{2}} = 0

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

\frac{x - 5}{3 x + 4} = \frac{x - 5}{2 x + 1}

T + \frac{a}{N}

\frac{16}{x ^{3}} = 0

What is the answer to 1/(3-x)=(x^2-9)/((x-3)^2) ?
The answer to 1/(3-x)=(x^2-9)/((x-3)^2) is x=-4
Solve for x: 1/(3-x)=(x^2-9)/((x-3)^2)
The solution is x=-4