<p><span style="font-size:22px"><a href="https://www.prepswift.com/quizzes/quiz/prepswift-simplifying-algebraic-expressions-2" target="_blank">Simplifying Algebraic Expressions 2 Exercise</a></span></p><p>Sometimes we can simplify complex roots like this:</p>
<p>$\sqrt{y^4-10y^2+25}$</p>
<p>We can use Identity 3 to recognize this is the same as $\sqrt{(y^2-5)^2}$ which is just $|y^2-5|$. We can only cancel the square root if we put the absolute value symbols ($|$ )around the result.</p>
<p>Some complex fractions can be simplified too, but they take a bit of thinking:</p>
<p>$\frac{2}{a^2-25}-\frac{1}{a^2+5a}$ </p>
<p>We can start by factoring out the denominators using our identities:</p>
<p>$\frac{2}{(a+5)(a-5)}-\frac{1}{a(a+5)}$</p>
<p>To get a common denominator (and cancel out what they don't share in common) we need to multiply the left by $\frac{a}{a}$ and the right by $\frac{a-5}{a-5}$. This will give both fractions a denominator of $a(a-5)(a+5)$:</p>
<p>$\frac{2a}{a(a-5)(a+5)}-\frac{a-5}{a(a-5)(a+5)} = \frac{2a-a+5}{a(a-5)(a+5)} = \frac{a+5}{a(a-5)(a+5)}$</p>
<p>Finally, we can cancel out the $a+5$ to get:</p>
<p>$\frac{1}{a(a-5)}$</p>
<p>Note that $a$ cannot equal $5$, $-5$, or $0$!</p>