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

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

Solve for x

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

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply 2x+1 by x+3 and combine like terms.

$$2x^{2}+3x-2=2x^{2}+7x+3$$

Subtract 2x^{2} from both sides.

$$2x^{2}+3x-2-2x^{2}=7x+3$$

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

$$3x-2=7x+3$$

Subtract 7x from both sides.

$$3x-2-7x=3$$

Combine 3x and -7x to get -4x.

$$-4x-2=3$$

Add 2 to both sides.

$$-4x=3+2$$

Add 3 and 2 to get 5.

$$-4x=5$$

Divide both sides by -4.

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

Fraction \frac{5}{-4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

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