What is the answer to x/(x+3)= 3/(x-3)+9 ?

The answer to x/(x+3)= 3/(x-3)+9 is x=(3(sqrt(65)-1))/8 ,x=-(3(1+sqrt(65)))/8

Solve for x: x/(x+3)= 3/(x-3)+9

The solution is x=(3(sqrt(65)-1))/8 ,x=-(3(1+sqrt(65)))/8

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\frac{x}{x + 3} = \frac{3}{x - 3} + 9

x = \frac{3 ( 65 - 1 )}{8}, x = - \frac{3 ( 1 + 65 )}{8}

Decimal Notation

x = 2.64834 \dots, x = - 3.39834 \dots

Solution steps

\frac{x}{x + 3} = \frac{3}{x - 3} + 9

Multiply by LCM

x (x - 3) = 3 (x + 3) + 9 (x + 3) (x - 3)

Solve

x (x - 3) = 3 (x + 3) + 9 (x + 3) (x - 3) : x = \frac{3 ( 65 - 1 )}{8}, x = - \frac{3 ( 1 + 65 )}{8}

x = \frac{3 ( 65 - 1 )}{8}, x = - \frac{3 ( 1 + 65 )}{8}

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 3

Combine undefined points with solutions:

x = \frac{3 ( 65 - 1 )}{8}, x = - \frac{3 ( 1 + 65 )}{8}

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

18 x - 77 = \frac{18}{x}

20 = \frac{x ^{2}}{75 - x}

x, a = \frac{y}{x - 1}

\frac{5}{x} = 8

What is the answer to x/(x+3)= 3/(x-3)+9 ?
The answer to x/(x+3)= 3/(x-3)+9 is x=(3(sqrt(65)-1))/8 ,x=-(3(1+sqrt(65)))/8
Solve for x: x/(x+3)= 3/(x-3)+9
The solution is x=(3(sqrt(65)-1))/8 ,x=-(3(1+sqrt(65)))/8