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

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

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,\frac{1}{4} since division by zero is not defined. Multiply both sides of the equation by \left(4x-1\right)\left(x+1\right), the least common multiple of 4x-1,x+1.

$$\left(x+1\right)\times 2=\left(4x-1\right)\times 3$$

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

$$2x+2=\left(4x-1\right)\times 3$$

Use the distributive property to multiply 4x-1 by 3.

$$2x+2=12x-3$$

Subtract 12x from both sides.

$$2x+2-12x=-3$$

Combine 2x and -12x to get -10x.

$$-10x+2=-3$$

Subtract 2 from both sides.

$$-10x=-3-2$$

Subtract 2 from -3 to get -5.

$$-10x=-5$$

Divide both sides by -10.

$$x=\frac{-5}{-10}$$

Reduce the fraction \frac{-5}{-10} to lowest terms by extracting and canceling out -5.

$$x=\frac{1}{2}$$