Solve x^2/(2-x)(10-x)=1

$$\frac { x ^ { 2 } } { ( 2 - x ) ( 10 - x ) } = 1$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 2,10 since division by zero is not defined. Multiply both sides of the equation by \left(x-10\right)\left(x-2\right).

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

Use the distributive property to multiply x-10 by x-2 and combine like terms.

$$x^{2}=x^{2}-12x+20$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=-12x+20$$

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

$$0=-12x+20$$

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

$$-12x+20=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-12x=-20$$

Divide both sides by -12.

$$x=\frac{-20}{-12}$$

Reduce the fraction \frac{-20}{-12} to lowest terms by extracting and canceling out -4.

$$x=\frac{5}{3}$$