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

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,3 since division by zero is not defined. Multiply both sides of the equation by x\left(x-3\right), the least common multiple of x-3,x^{2}-3x.

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

Multiply x and x to get x^{2}.

$$x^{2}+x\left(x-3\right)\left(-1\right)=4-x$$

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

$$x^{2}+\left(x^{2}-3x\right)\left(-1\right)=4-x$$

Use the distributive property to multiply x^{2}-3x by -1.

$$x^{2}-x^{2}+3x=4-x$$

Combine x^{2} and -x^{2} to get 0.

$$3x=4-x$$

Add x to both sides.

$$3x+x=4$$

Combine 3x and x to get 4x.

$$4x=4$$

Divide both sides by 4.

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

Divide 4 by 4 to get 1.

$$x=1$$