Solve 1/4+1/b=b+1/b^2

$$\frac { 1 } { 4 } + \frac { 1 } { b } = \frac { b + 1 } { b ^ { 2 } }$$

Solve for b

$$b=-2$$

$$b=2$$

Steps Using Difference of Squares

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4b^{2}, the least common multiple of 4,b,b^{2}.

$$4b^{2}\times \frac{1}{4}+4b=4\left(b+1\right)$$

Multiply 4 and \frac{1}{4} to get 1.

$$b^{2}+4b=4\left(b+1\right)$$

Use the distributive property to multiply 4 by b+1.

$$b^{2}+4b=4b+4$$

Subtract 4b from both sides.

$$b^{2}+4b-4b=4$$

Combine 4b and -4b to get 0.

$$b^{2}=4$$

Subtract 4 from both sides.

$$b^{2}-4=0$$

Consider b^{2}-4. Rewrite b^{2}-4 as b^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(b-2\right)\left(b+2\right)=0$$

To find equation solutions, solve b-2=0 and b+2=0.

$$b=2 b=-2$$

Steps by Finding Square Root

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4b^{2}, the least common multiple of 4,b,b^{2}.

$$4b^{2}\times \frac{1}{4}+4b=4\left(b+1\right)$$

Multiply 4 and \frac{1}{4} to get 1.

$$b^{2}+4b=4\left(b+1\right)$$

Use the distributive property to multiply 4 by b+1.

$$b^{2}+4b=4b+4$$

Subtract 4b from both sides.

$$b^{2}+4b-4b=4$$

Combine 4b and -4b to get 0.

$$b^{2}=4$$

Take the square root of both sides of the equation.

$$b=2 b=-2$$

Steps Using the Quadratic Formula

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4b^{2}, the least common multiple of 4,b,b^{2}.

$$4b^{2}\times \frac{1}{4}+4b=4\left(b+1\right)$$

Multiply 4 and \frac{1}{4} to get 1.

$$b^{2}+4b=4\left(b+1\right)$$

Use the distributive property to multiply 4 by b+1.

$$b^{2}+4b=4b+4$$

Subtract 4b from both sides.

$$b^{2}+4b-4b=4$$

Combine 4b and -4b to get 0.

$$b^{2}=4$$

Subtract 4 from both sides.

$$b^{2}-4=0$$

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

$$b=\frac{0±\sqrt{0^{2}-4\left(-4\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-4\right)}}{2}$$

Multiply -4 times -4.

$$b=\frac{0±\sqrt{16}}{2}$$

Take the square root of 16.

$$b=\frac{0±4}{2}$$

Now solve the equation b=\frac{0±4}{2} when ± is plus. Divide 4 by 2.

$$b=2$$

Now solve the equation b=\frac{0±4}{2} when ± is minus. Divide -4 by 2.

$$b=-2$$

The equation is now solved.

$$b=2 b=-2$$