Simplify and state any excluded values? C-5/C^2-25

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Answer 1 · 2018-07-29T15:23:17

$color(purple)(=>1/(c + 5)$ for $color(crimson)(c != 5$

$(c - 5) / (c^2 - 25)$

$=> cancel(c - 5)^color(red)(1) / ((c + 5) cancel(c - 5))$

$=> 1 / (c + 5)$ for $c != 5$

As when $c = 5$ , Numerator and Denominator become $0$ .

Hence the term becomes $=>0/0$ which is indeterminant.

Answer 2 · 2018-07-29T15:50:11

$1/(c+5), c!=5$

We have the following:

$(c-5)/(c^2-25)$

Notice that the denominator is a difference of squares

$a^2-b^2$ , that can be factored as $(a+b)(a-b)$ . This simplifies to

$color(blue)((c-5)/((c+5)(c-5)))$

We can cancel out common factors on the top and bottom to get

$cancel(c-5)/((c+5)cancel(c-5))=1/(c+5)$

Recall that in the initial expression (blue), if $c=5$ , that would make this expression undefined, as we would get indeterminate form

$0/0$

Because of this, in our simplified expression, $c$ still cannot be $5$ .

$1/(c+5), c!=5$

Hope this helps!