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

The answer to 1/(x+3)-1/x =5 is x=(-15+sqrt(165))/(10),x=(-15-sqrt(165))/(10)

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

The solution is x=(-15+sqrt(165))/(10),x=(-15-sqrt(165))/(10)

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

x = \frac{- 15 + 165}{10}, x = \frac{- 15 - 165}{10}

Decimal

x = - 0.21547 \dots, x = - 2.78452 \dots

Solution steps

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

Multiply by LCM

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

Solve

x - (x + 3) = 5 x (x + 3) : x = \frac{- 15 + 165}{10}, x = \frac{- 15 - 165}{10}

x = \frac{- 15 + 165}{10}, x = \frac{- 15 - 165}{10}

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 0

Combine undefined points with solutions:

x = \frac{- 15 + 165}{10}, x = \frac{- 15 - 165}{10}

- 7 - \frac{3}{x} = - 6 x

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

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

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

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

What is the answer to 1/(x+3)-1/x =5 ?
The answer to 1/(x+3)-1/x =5 is x=(-15+sqrt(165))/(10),x=(-15-sqrt(165))/(10)
Solve for x: 1/(x+3)-1/x =5
The solution is x=(-15+sqrt(165))/(10),x=(-15-sqrt(165))/(10)