Solve x/x-3-6/x^2-2x-3=1

$$\frac{ x }{ x-3 } - \frac{ 6 }{ { x }^{ 2 } -2x-3 } = 1$$

Solve for x

$$x=1$$

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-3,x^{2}-2x-3.

$$\left(x+1\right)x-6=\left(x-3\right)\left(x+1\right)$$

Use the distributive property to multiply x+1 by x.

$$x^{2}+x-6=\left(x-3\right)\left(x+1\right)$$

Use the distributive property to multiply x-3 by x+1 and combine like terms.

$$x^{2}+x-6=x^{2}-2x-3$$

Subtract x^{2} from both sides.

$$x^{2}+x-6-x^{2}=-2x-3$$

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

$$x-6=-2x-3$$

Add 2x to both sides.

$$x-6+2x=-3$$

Combine x and 2x to get 3x.

$$3x-6=-3$$

Add 6 to both sides.

$$3x=-3+6$$

Add -3 and 6 to get 3.

$$3x=3$$

Divide both sides by 3.

$$x=\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$x=1$$