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

Determine whether the expression is true or false:

$\frac{a\cdot b}{c\cdot a}=\frac{c}{b}$

Let's examine the problem:

$\frac{a\cdot b}{c\cdot a} \stackrel{?}{= } \frac{c}{b}$Note that we can simplify the expression on the left side, this can be done by reducing the fraction:

$\frac{\not{a}\cdot b}{c\cdot \not{a}} =\\ \boxed{\frac{b}{c}}$However the expression on the right side is:

$\frac{c}{b}$Therefore the expressions on both sides of the (assumed) equation are not equal, meaning:

$\frac{a\cdot b}{c\cdot a}=\frac{b}{c} \stackrel{!}{\neq } \frac{c}{b}$

(In other words, there is no identity equation- which is true for all possible parameter values $a,b,c$)

Therefore the correct answer is answer B.