Solve x/x-5-1/x^2-11x+30=x/x-6

$$\frac { x } { x - 5 } - \frac { 1 } { x ^ { 2 } - 11 x + 30 } = \frac { x } { x - 6 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 5,6 since division by zero is not defined. Multiply both sides of the equation by \left(x-6\right)\left(x-5\right), the least common multiple of x-5,x^{2}-11x+30,x-6.

$$\left(x-6\right)x-1=\left(x-5\right)x$$

Use the distributive property to multiply x-6 by x.

$$x^{2}-6x-1=\left(x-5\right)x$$

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

$$x^{2}-6x-1=x^{2}-5x$$

Subtract x^{2} from both sides.

$$x^{2}-6x-1-x^{2}=-5x$$

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

$$-6x-1=-5x$$

Add 5x to both sides.

$$-6x-1+5x=0$$

Combine -6x and 5x to get -x.

$$-x-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$-x=1$$

Multiply both sides by -1.

$$x=-1$$