What is the answer to 5/6 =r-6/(r+3) ?

The answer to 5/6 =r-6/(r+3) is r=(-13+sqrt(1393))/(12),r=(-13-sqrt(1393))/(12)

Solve for r: 5/6 =r-6/(r+3)

The solution is r=(-13+sqrt(1393))/(12),r=(-13-sqrt(1393))/(12)

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\frac{5}{6} = r - \frac{6}{r + 3}

r = \frac{- 13 + 1393}{12}, r = \frac{- 13 - 1393}{12}

Decimal Notation

r = 2.02690 \dots, r = - 4.19357 \dots

Solution steps

\frac{5}{6} = r - \frac{6}{r + 3}

Multiply by LCM

5 (r + 3) = r \cdot 6 (r + 3) - 36

Solve

5 (r + 3) = r \cdot 6 (r + 3) - 36 : r = \frac{- 13 + 1393}{12}, r = \frac{- 13 - 1393}{12}

r = \frac{- 13 + 1393}{12}, r = \frac{- 13 - 1393}{12}

Verify Solutions

Find undefined (singularity) points:

r = - 3

Combine undefined points with solutions:

r = \frac{- 13 + 1393}{12}, r = \frac{- 13 - 1393}{12}

\frac{r - 4}{5 r} = \frac{1}{5 r} + 1

\frac{26}{x} = - 13

\frac{x + 4}{x} = 81

\frac{x}{3} + \frac{5}{x - 5} = 0

\frac{8}{x} = 2 x

What is the answer to 5/6 =r-6/(r+3) ?
The answer to 5/6 =r-6/(r+3) is r=(-13+sqrt(1393))/(12),r=(-13-sqrt(1393))/(12)
Solve for r: 5/6 =r-6/(r+3)
The solution is r=(-13+sqrt(1393))/(12),r=(-13-sqrt(1393))/(12)