Solve 5/x-4x+3+2/x-1-4/x-3=0

$$\frac { 5 } { x - 4 x + 3 } + \frac { 2 } { x - 1 } - \frac { 4 } { x - 3 } = 0$$

Solve for x

$$x=\frac{9}{11}\approx 0.818181818$$

Steps for Solving Linear Equation

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

$$\left(3-x\right)\times 5+\left(3x-9\right)\times 2-\left(3x-3\right)\times 4=0$$

Use the distributive property to multiply 3-x by 5.

$$15-5x+\left(3x-9\right)\times 2-\left(3x-3\right)\times 4=0$$

Use the distributive property to multiply 3x-9 by 2.

$$15-5x+6x-18-\left(3x-3\right)\times 4=0$$

Combine -5x and 6x to get x.

$$15+x-18-\left(3x-3\right)\times 4=0$$

Subtract 18 from 15 to get -3.

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

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

$$-3+x-\left(12x-12\right)=0$$

To find the opposite of 12x-12, find the opposite of each term.

$$-3+x-12x+12=0$$

Combine x and -12x to get -11x.

$$-3-11x+12=0$$

Add -3 and 12 to get 9.

$$9-11x=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-11x=-9$$

Divide both sides by -11.

$$x=\frac{-9}{-11}$$

Fraction \frac{-9}{-11} can be simplified to \frac{9}{11} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{9}{11}$$