Verify the Fraction Equation: Is (a·b)/(c·a) = c/b True or False?

You can cancel a variable when it appears as a factor in both the numerator and denominator. In $\frac{a \cdot b}{c \cdot a}$, the variable a multiplies both parts, so it cancels out.

These are reciprocals of each other! $\frac{b}{c}$ and $\frac{c}{b}$ are only equal when b = c. For example, $\frac{2}{3} \neq \frac{3}{2}$.

Yes! Try a = 2, b = 3, c = 4. Left side: $\frac{2 \cdot 3}{4 \cdot 2} = \frac{6}{8} = \frac{3}{4}$. Right side: $\frac{4}{3}$. Since $\frac{3}{4} \neq \frac{4}{3}$, the equation is false.

An identity is true for all possible values of the variables. Since our equation gives different results for the left and right sides, it's not an identity.

Simplifying reveals the true form of an expression. Without simplifying $\frac{a \cdot b}{c \cdot a}$ to $\frac{b}{c}$, you might miss that it's different from $\frac{c}{b}$.