Question

In the following exercises, simplify each rational expression. $\frac{z^2-9 z+20}{16-z^2}$

   In the following exercises, simplify each rational expression.
$\frac{z^2-9 z+20}{16-z^2}$
Intermediate Algebra
Intermediate Algebra
Lynn Marecek 1st Edition
Chapter 7, Problem 27 ↓
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In the following exercises, simplify each rational expression. $\frac{z^2-9 z+20}{16-z^2}$
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Transcript

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00:01 For this problem, the first thing we need to do is completely factor.
00:05 So on the top, this trinomial factors out to be z minus 4 and z minus 5.
00:15 And then on the bottom, before we factor this, this is a difference of squares, but before we factor this, i just want to rearrange the terms so that the variable is listed first.
00:27 So we have negative z squared plus 16.
00:33 And then in order to do that, i need to factor out a negative 1 because we always want our variable term to be a positive term.
00:42 Our leading variable term, i should say, should always be positive.
00:46 So we're going to factor out a negative 1, and that's going to turn this into positive z squared minus 16.
00:55 So now that we've done that, we can factor this difference of squares.
00:59 We're going to keep the negative 1 in front, and this is going to become z plus.
01:05 And z minus four when we use the difference of squares formula.
01:11 So now that everything's factored, i'm just going to rewrite it so that it's a little bit more concise, rewriting everything in fully factored form...
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