Solve 3x+4/x^2+x-2=4/x-1+5/x+2

$$\frac { 3 x + 4 } { x ^ { 2 } + x - 2 } = \frac { 4 } { x - 1 } + \frac { 5 } { x + 2 }$$

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

Steps for Solving Linear Equation

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

$$3x+4=\left(x+2\right)\times 4+\left(x-1\right)\times 5$$

Use the distributive property to multiply x+2 by 4.

$$3x+4=4x+8+\left(x-1\right)\times 5$$

Use the distributive property to multiply x-1 by 5.

$$3x+4=4x+8+5x-5$$

Combine 4x and 5x to get 9x.

$$3x+4=9x+8-5$$

Subtract 5 from 8 to get 3.

$$3x+4=9x+3$$

Subtract 9x from both sides.

$$3x+4-9x=3$$

Combine 3x and -9x to get -6x.

$$-6x+4=3$$

Subtract 4 from both sides.

$$-6x=3-4$$

Subtract 4 from 3 to get -1.

$$-6x=-1$$

Divide both sides by -6.

$$x=\frac{-1}{-6}$$

Fraction \frac{-1}{-6} can be simplified to \frac{1}{6} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{6}$$