Checkpoint: Rational Equations: Proportions Solution

Solve.

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

$\begin{array}{rcl} a \neq - 1, 2 \\ (a - 2) (a - 2) & = & (a + 1) (a - 1) \\ a^{2} - 4 a + 4 & = & a^{2} - 1 \\ - 4 a & = & - 5 \\ a & = & \frac{5}{4} \end{array}$

Note

Q: Why is it not possible to simplify the expression $(a - 2)$ from the equation as the first step?
A: Because you cannot simplify on opposite sides of the equal sign in an equation. 

Q: How can you determine if the value or values you solved for are correct?
A: Substitute them into the given problem to see if both sides of the equation are equal to one another.