Why simplifying this function generates different outputs for same input?

[gen x]

This function $f(x) = \frac{x^2 - 4}{x - 2}$ when simplify become $f(x) = x + 2$ .

If I enter $x=2$ in the first expression I get $y=\frac{0}{0}$, and if I enter $x=2$ in the second expression I get $y=4$.


Why different results if this is same function, just simplifly?

 

[kuruman]

Why different results if this is same function, just simplifly?

Because you cannot "just simplify" unless you specifically exclude $x=2$ at which point, as you have discovered, the function is undefined. In other words, the two functions are "the same" except at $x=2.$

What would you say to someone who argues that, for any $a$, $$f(2)=\frac{2^2-4}{2-2}=\frac{0}{0}=\frac{0\cdot a}{0}=\frac{\cancel{0}\cdot a}{\cancel{0}}=a~~?$$

 

[Mark44]

This function $f(x) = \frac{x^2 - 4}{x - 2}$ when simplify become $f(x) = x + 2$ .

If I enter $x=2$ in the first expression I get $y=\frac{0}{0}$, and if I enter $x=2$ in the second expression I get $y=4$.


Why different results if this is same function, just simplifly?

The two functions are identical except at the point (2, 4). The graph of $f(x) = \frac{x^2 - 4}{x - 2}$ can be thought of as a straight line whose slope is 1 and with a y-intercept of 2, but with a "hole" at (2, 4).

 

[FactChecker]

Good catch! You did very well to check the final answers in the original formula. As you go through a simplification, you should keep track of any values of x where the original function was undefined. That can become difficult and tricky. It is wise to check your results in the original formula.