What is the answer to 3/(2b)+(2b)/(b-3)=2 ?

The answer to 3/(2b)+(2b)/(b-3)=2 is b= 3/5

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3/(2b)+(2b)/(b-3)=2

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

b = \frac{3}{5}

Decimal Notation

b = 0.6

Solution steps

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

Multiply by LCM

3 (b - 3) + 4 b^{2} = 4 b (b - 3)

Expand

3 (b - 3) : 3 b - 9

3 b - 9 + 4 b^{2} = 4 b (b - 3)

Expand

4 b (b - 3) : 4 b^{2} - 12 b

3 b - 9 + 4 b^{2} = 4 b^{2} - 12 b

Move

9

to the right side

3 b + 4 b^{2} = 4 b^{2} - 12 b + 9

Subtract

4 b^{2} - 12 b

from both sides

3 b + 4 b^{2} - (4 b^{2} - 12 b) = 4 b^{2} - 12 b + 9 - (4 b^{2} - 12 b)

Simplify

15 b = 9

Divide both sides by

15

b = \frac{3}{5}

Verify Solutions

Find undefined (singularity) points:

b = 0, b = 3

Combine undefined points with solutions:

b = \frac{3}{5}

\frac{2 y - 4}{y + 7} = \frac{1}{3}

\frac{14}{x} = \frac{1}{12}

\frac{9}{x} = \frac{x}{4}

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

x + \frac{1}{x} = 45

What is the answer to 3/(2b)+(2b)/(b-3)=2 ?
The answer to 3/(2b)+(2b)/(b-3)=2 is b= 3/5
Solve for b: 3/(2b)+(2b)/(b-3)=2
The solution is b= 3/5