What is the answer to (2x)/(x-5)+1/(x-3)=3 ?

The answer to (2x)/(x-5)+1/(x-3)=3 is x=(19-sqrt(161))/2 ,x=(19+sqrt(161))/2

Solve for x: (2x)/(x-5)+1/(x-3)=3

The solution is x=(19-sqrt(161))/2 ,x=(19+sqrt(161))/2

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

x = \frac{19 - 161}{2}, x = \frac{19 + 161}{2}

Decimal Notation

x = 3.15571 \dots, x = 15.84428 \dots

Solution steps

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

Multiply by LCM

2 x (x - 3) + x - 5 = 3 (x - 5) (x - 3)

Solve

2 x (x - 3) + x - 5 = 3 (x - 5) (x - 3) : x = \frac{19 - 161}{2}, x = \frac{19 + 161}{2}

x = \frac{19 - 161}{2}, x = \frac{19 + 161}{2}

Verify Solutions

Find undefined (singularity) points:

x = 5, x = 3

Combine undefined points with solutions:

x = \frac{19 - 161}{2}, x = \frac{19 + 161}{2}

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

\frac{9 x + 10}{3 x - 8} = \frac{12 x - 8}{4 x - 5}

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

1 + \frac{2}{x - 3} = \frac{5}{x ^{2} - 9}

2 x^{- 3} = 54

What is the answer to (2x)/(x-5)+1/(x-3)=3 ?
The answer to (2x)/(x-5)+1/(x-3)=3 is x=(19-sqrt(161))/2 ,x=(19+sqrt(161))/2
Solve for x: (2x)/(x-5)+1/(x-3)=3
The solution is x=(19-sqrt(161))/2 ,x=(19+sqrt(161))/2