Solve x+4/6x^2+x-2-3/8x-4=0

$$\frac { x + 4 } { 6 x ^ { 2 } + x - 2 } - \frac { 3 } { 8 x - 4 } = 0$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{2}{3},\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 4\left(2x-1\right)\left(3x+2\right), the least common multiple of 6x^{2}+x-2,8x-4.

$$4\left(x+4\right)-\left(3x+2\right)\times 3=0$$

Use the distributive property to multiply 4 by x+4.

$$4x+16-\left(3x+2\right)\times 3=0$$

Use the distributive property to multiply 3x+2 by 3.

$$4x+16-\left(9x+6\right)=0$$

To find the opposite of 9x+6, find the opposite of each term.

$$4x+16-9x-6=0$$

Combine 4x and -9x to get -5x.

$$-5x+16-6=0$$

Subtract 6 from 16 to get 10.

$$-5x+10=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-5x=-10$$

Divide both sides by -5.

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

Divide -10 by -5 to get 2.

$$x=2$$