Solve 3/2b+2b/b-3=2

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

Solve for b

$$b=\frac{3}{5}=0.6$$

Steps for Solving Linear Equation

Variable b cannot be equal to any of the values 0,3 since division by zero is not defined. Multiply both sides of the equation by 2b\left(b-3\right), the least common multiple of 2b,b-3.

$$\left(b-3\right)\times 3+2b\times 2b=4b\left(b-3\right)$$

Multiply 2b and 2b to get \left(2b\right)^{2}.

$$\left(b-3\right)\times 3+\left(2b\right)^{2}=4b\left(b-3\right)$$

Use the distributive property to multiply b-3 by 3.

$$3b-9+\left(2b\right)^{2}=4b\left(b-3\right)$$

Expand \left(2b\right)^{2}.

$$3b-9+2^{2}b^{2}=4b\left(b-3\right)$$

Calculate 2 to the power of 2 and get 4.

$$3b-9+4b^{2}=4b\left(b-3\right)$$

Use the distributive property to multiply 4b by b-3.

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

Subtract 4b^{2} from both sides.

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

Combine 4b^{2} and -4b^{2} to get 0.

$$3b-9=-12b$$

Add 12b to both sides.

$$3b-9+12b=0$$

Combine 3b and 12b to get 15b.

$$15b-9=0$$

Add 9 to both sides. Anything plus zero gives itself.

$$15b=9$$

Divide both sides by 15.

$$b=\frac{9}{15}$$

Reduce the fraction \frac{9}{15} to lowest terms by extracting and canceling out 3.

$$b=\frac{3}{5}$$