What is the answer to (v^2+v)/(2v+1)=v-3 ?

The answer to (v^2+v)/(2v+1)=v-3 is v=3+2sqrt(3),v=3-2sqrt(3)

Solve for v: (v^2+v)/(2v+1)=v-3

The solution is v=3+2sqrt(3),v=3-2sqrt(3)

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\frac{v ^{2} + v}{2 v + 1} = v - 3

v = 3 + 23, v = 3 - 23

Decimal Notation

v = 6.46410 \dots, v = - 0.46410 \dots

Solution steps

\frac{v ^{2} + v}{2 v + 1} = v - 3

Multiply both sides by

2 v + 1

v^{2} + v = v (2 v + 1) - 3 (2 v + 1)

Solve

v^{2} + v = v (2 v + 1) - 3 (2 v + 1) : v = 3 + 23, v = 3 - 23

v = 3 + 23, v = 3 - 23

Verify Solutions

Find undefined (singularity) points:

v = - \frac{1}{2}

Combine undefined points with solutions:

v = 3 + 23, v = 3 - 23

\frac{2 x - 7}{2 x + 4} = \frac{2}{3}

\frac{1}{x} - 3 = 0

\frac{7}{x + 2} = \frac{5}{x - 5}

1 + \frac{4 x}{x - 8} = \frac{7}{x - 8}

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

What is the answer to (v^2+v)/(2v+1)=v-3 ?
The answer to (v^2+v)/(2v+1)=v-3 is v=3+2sqrt(3),v=3-2sqrt(3)
Solve for v: (v^2+v)/(2v+1)=v-3
The solution is v=3+2sqrt(3),v=3-2sqrt(3)