Verify if (ab+c)/(c+ab) = 1: Rational Expression Analysis

Indicate whether true or false$\frac{a\cdot b+c}{c+a\cdot b}=1$

Let's first examine the problem:

$\frac{ab+c}{c+a b}\stackrel{?}{= }1$Looking at the expression on the left side, note that direct use of the distributive property in addition in the fraction's numerator (or alternatively in its denominator) gives us:

$\frac{a b+c}{c+a b}=\\ \frac{c+a b}{c+ab}=\\ 1$where in the final step we used the fact that dividing any number by itself always yields 1,

Therefore, the expressions on both sides of the (assumed) equality are indeed equal, meaning:

$\frac{a b+c}{c+a b}= \frac{c+a b}{c+ab}\stackrel{!}{= }1$

(In other words, an identity equation holds- which is true for all possible values of the parameter $a,b,c$)

Therefore, the correct answer is answer A.