Solve a^2/a-1=a-1

$$\frac { a ^ { 2 } } { a - 1 } = a - 1$$

Solve for a

$$a=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Variable a cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by a-1.

$$a^{2}=\left(a-1\right)a+\left(a-1\right)\left(-1\right)$$

Use the distributive property to multiply a-1 by a.

$$a^{2}=a^{2}-a+\left(a-1\right)\left(-1\right)$$

Use the distributive property to multiply a-1 by -1.

$$a^{2}=a^{2}-a-a+1$$

Combine -a and -a to get -2a.

$$a^{2}=a^{2}-2a+1$$

Subtract a^{2} from both sides.

$$a^{2}-a^{2}=-2a+1$$

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

$$0=-2a+1$$

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

$$-2a+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-2a=-1$$

Divide both sides by -2.

$$a=\frac{-1}{-2}$$

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

$$a=\frac{1}{2}$$