Solve 4/2x+1=6x-1/3x^2+1

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

Solve for x

$$x = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x+1\right)\left(3x^{2}+1\right), the least common multiple of 2x+1,3x^{2}+1.

$$\left(3x^{2}+1\right)\times 4=\left(2x+1\right)\left(6x-1\right)$$

Use the distributive property to multiply 3x^{2}+1 by 4.

$$12x^{2}+4=\left(2x+1\right)\left(6x-1\right)$$

Use the distributive property to multiply 2x+1 by 6x-1 and combine like terms.

$$12x^{2}+4=12x^{2}+4x-1$$

Subtract 12x^{2} from both sides.

$$12x^{2}+4-12x^{2}=4x-1$$

Combine 12x^{2} and -12x^{2} to get 0.

$$4=4x-1$$

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

$$4x-1=4$$

Add 1 to both sides.

$$4x=4+1$$

Add 4 and 1 to get 5.

$$4x=5$$

Divide both sides by 4.

$$x=\frac{5}{4}$$