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

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

Solve for x

$$x\neq -\frac{1}{2}$$

Solution Steps

Variable x cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2x+1.

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

Use the distributive property to multiply -x by 2x+1.

$$2x^{2}+3x+1-2x^{2}-x=2x+1$$

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

$$3x+1-x=2x+1$$

Combine 3x and -x to get 2x.

$$2x+1=2x+1$$

Subtract 2x from both sides.

$$2x+1-2x=1$$

Combine 2x and -2x to get 0.

$$1=1$$

Compare 1 and 1.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to -\frac{1}{2}.

$$x\in \mathrm{R}\setminus -\frac{1}{2}$$