Simplifying Algebraic Expressions 2

<a href="https://www.prepswift.com/quizzes/quiz/prepswift-simplifying-algebraic-expressions-2" target="_blank">Simplifying Algebraic Expressions 2 Exercise</a>Sometimes we can simplify complex roots like this: $\sqrt{y^4-10y^2+25}$ 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. Some complex fractions can be simplified too, but they take a bit of thinking: $\frac{2}{a^2-25}-\frac{1}{a^2+5a}$  We can start by factoring out the denominators using our identities: $\frac{2}{(a+5)(a-5)}-\frac{1}{a(a+5)}$ 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 $a(a-5)(a+5)$: $\frac{2a}{a(a-5)(a+5)}-\frac{a-5}{a(a-5)(a+5)} = \frac{2a-a+5}{a(a-5)(a+5)} = \frac{a+5}{a(a-5)(a+5)}$ Finally, we can cancel out the $a+5$ to get: $\frac{1}{a(a-5)}$ Note that $a$ cannot equal $5$, $-5$, or $0$!