What is the simplified form of $(x^2-25)/(x-5)$ ?

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Answer 1 · 2015-09-13T13:33:53

$(x^2-25)/(x-5) = x+5$ with exclusion $x != 5$

Use the difference of squares identity:

$a^2-b^2 = (a-b)(a+b)$

to find:

$(x^2-25)/(x-5) = (x^2-5^2)/(x-5) = ((x-5)(x+5))/(x-5)$

$= (x-5)/(x-5)*(x+5) = x+5$

with exclusion $x != 5$

Note that if $x = 5$ then both $(x^2-25)$ and $(x-5)$ are $0$ , so $(x^2-25)/(x-5) = 0/0$ is undefined.

What is the simplified form of (x^2-25)/(x-5)(x^2-25)/(x-5)?