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

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

Solve for x

$$x=2$$

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 \left(x-3\right)\left(x-1\right), the least common multiple of x-1,x-3,x^{2}-4x+3.

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

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

$$3x-9-\left(x-1\right)=-4$$

To find the opposite of x-1, find the opposite of each term.

$$3x-9-x+1=-4$$

Combine 3x and -x to get 2x.

$$2x-9+1=-4$$

Add -9 and 1 to get -8.

$$2x-8=-4$$

Add 8 to both sides.

$$2x=-4+8$$

Add -4 and 8 to get 4.

$$2x=4$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x=2$$