Solve 3b^2+2b/b^2-4=b/b-2

$$\frac { 3 b ^ { 2 } + 2 b } { b ^ { 2 } - 4 } = \frac { b } { b - 2 }$$

Solve for b

$$b=0$$

Steps by Finding Square Root

Variable b cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by \left(b-2\right)\left(b+2\right), the least common multiple of b^{2}-4,b-2.

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

Use the distributive property to multiply b+2 by b.

$$3b^{2}+2b=b^{2}+2b$$

Subtract b^{2} from both sides.

$$3b^{2}+2b-b^{2}=2b$$

Combine 3b^{2} and -b^{2} to get 2b^{2}.

$$2b^{2}+2b=2b$$

Subtract 2b from both sides.

$$2b^{2}+2b-2b=0$$

Combine 2b and -2b to get 0.

$$2b^{2}=0$$

Divide both sides by 2. Zero divided by any non-zero number gives zero.

$$b^{2}=0$$

Take the square root of both sides of the equation.

$$b=0 b=0$$

The equation is now solved. Solutions are the same.

$$b=0$$

Steps Using the Quadratic Formula

Variable b cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by \left(b-2\right)\left(b+2\right), the least common multiple of b^{2}-4,b-2.

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

Use the distributive property to multiply b+2 by b.

$$3b^{2}+2b=b^{2}+2b$$

Subtract b^{2} from both sides.

$$3b^{2}+2b-b^{2}=2b$$

Combine 3b^{2} and -b^{2} to get 2b^{2}.

$$2b^{2}+2b=2b$$

Subtract 2b from both sides.

$$2b^{2}+2b-2b=0$$

Combine 2b and -2b to get 0.

$$2b^{2}=0$$

Divide both sides by 2. Zero divided by any non-zero number gives zero.

$$b^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$b=\frac{0±0}{2}$$

Divide 0 by 2.

$$b=0$$