Solve 1+6/4b^2+3/2b^2=b+4/2b^2

$$\frac { 1 + 6 } { 4 b ^ { 2 } } + \frac { 3 } { 2 b ^ { 2 } } = \frac { b + 4 } { 2 b ^ { 2 } }$$

Solve for b

$$b = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

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 4b^{2},2b^{2}.

$$1+6+2\times 3=2\left(b+4\right)$$

Add 1 and 6 to get 7.

$$7+2\times 3=2\left(b+4\right)$$

Multiply 2 and 3 to get 6.

$$7+6=2\left(b+4\right)$$

Add 7 and 6 to get 13.

$$13=2\left(b+4\right)$$

Use the distributive property to multiply 2 by b+4.

$$13=2b+8$$

Swap sides so that all variable terms are on the left hand side.

$$2b+8=13$$

Subtract 8 from both sides.

$$2b=13-8$$

Subtract 8 from 13 to get 5.

$$2b=5$$

Divide both sides by 2.

$$b=\frac{5}{2}$$