What is the answer to 4/r =(2r-1)/(r+2) ?

The answer to 4/r =(2r-1)/(r+2) is r=(5+sqrt(89))/4 ,r=(5-sqrt(89))/4

Solve for r: 4/r =(2r-1)/(r+2)

The solution is r=(5+sqrt(89))/4 ,r=(5-sqrt(89))/4

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\frac{4}{r} = \frac{2 r - 1}{r + 2}

r = \frac{5 + 89}{4}, r = \frac{5 - 89}{4}

Decimal Notation

r = 3.60849 \dots, r = - 1.10849 \dots

Solution steps

\frac{4}{r} = \frac{2 r - 1}{r + 2}

Cross multiply

4 (r + 2) = r (2 r - 1)

Solve

4 (r + 2) = r (2 r - 1) : r = \frac{5 + 89}{4}, r = \frac{5 - 89}{4}

r = \frac{5 + 89}{4}, r = \frac{5 - 89}{4}

Verify Solutions

Find undefined (singularity) points:

r = 0, r = - 2

Combine undefined points with solutions:

r = \frac{5 + 89}{4}, r = \frac{5 - 89}{4}

\frac{7}{( t + 4 ) ^{2}} = 0

\frac{2 y}{y - 3} = - \frac{1}{y}

\frac{10}{x - 2} - \frac{3}{x} = 2

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

\frac{- 2 - \frac{8}{13}}{x + 2} = 1

What is the answer to 4/r =(2r-1)/(r+2) ?
The answer to 4/r =(2r-1)/(r+2) is r=(5+sqrt(89))/4 ,r=(5-sqrt(89))/4
Solve for r: 4/r =(2r-1)/(r+2)
The solution is r=(5+sqrt(89))/4 ,r=(5-sqrt(89))/4