Solve x^2/x-10=x-11

$$\frac { x ^ { 2 } } { x - 10 } = x - 11$$

Solve for x

$$x = \frac{110}{21} = 5\frac{5}{21} \approx 5.238095238$$

Steps for Solving Linear Equation

Variable x cannot be equal to 10 since division by zero is not defined. Multiply both sides of the equation by x-10.

$$x^{2}=\left(x-10\right)x+\left(x-10\right)\left(-11\right)$$

Use the distributive property to multiply x-10 by x.

$$x^{2}=x^{2}-10x+\left(x-10\right)\left(-11\right)$$

Use the distributive property to multiply x-10 by -11.

$$x^{2}=x^{2}-10x-11x+110$$

Combine -10x and -11x to get -21x.

$$x^{2}=x^{2}-21x+110$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=-21x+110$$

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

$$0=-21x+110$$

Swap sides so that all variable terms are on the left hand side.

$$-21x+110=0$$

Subtract 110 from both sides. Anything subtracted from zero gives its negation.

$$-21x=-110$$

Divide both sides by -21.

$$x=\frac{-110}{-21}$$

Fraction \frac{-110}{-21} can be simplified to \frac{110}{21} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{110}{21}$$