What is the answer to (r-4)/(5r)= 1/(5r)+1 ?

The answer to (r-4)/(5r)= 1/(5r)+1 is r=-5/4

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(r-4)/(5r)= 1/(5r)+1

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

r = - \frac{5}{4}

Decimal Notation

r = - 1.25

Solution steps

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

Multiply both sides by

5 r

r - 4 = 1 + 5 r

Move

4

to the right side

r = 5 r + 5

Move

5 r

to the left side

- 4 r = 5

Divide both sides by

- 4

r = - \frac{5}{4}

Verify Solutions

Find undefined (singularity) points:

r = 0

Combine undefined points with solutions:

r = - \frac{5}{4}

\frac{26}{x} = - 13

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

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

\frac{8}{x} = 2 x

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

What is the answer to (r-4)/(5r)= 1/(5r)+1 ?
The answer to (r-4)/(5r)= 1/(5r)+1 is r=-5/4
Solve for r: (r-4)/(5r)= 1/(5r)+1
The solution is r=-5/4