Verify the Fraction Equation: Is (a-b)/(c-b) = a/c True?

Indicate whether the following expression is true or false:

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

Let's begin by examining the problem:

$\frac{a-b}{c-b}\stackrel{?}{= }\frac{a}{c}$

Note that the expression on the left side cannot be simplified, despite the fact that both in the numerator and denominator there is the term $b$ . This is due to the fact that it is missing from the second term (both in numerator and denominator) and does not multiply it. Therefore the simplification - which is in fact - applying the division operation which is the inverse operation of multiplication, is not possible, and therefore the current form of the expression on the left side:

$\frac{a-b}{c-b}$

is its final and most simplified form,

The term on the right side is:

$\frac{a}{c}$

Therefore the expressions on both sides of the (assumed) equality are not equal, meaning:

$\frac{a-b}{c-b}\stackrel{!}{\neq }\frac{a}{c}$

(In other words, there is no identical equality- that is true for all possible values of the parameters $a,b,c$)

Therefore, the correct answer is answer B.