<s>[INST] Practice test - simplifying expressions another question I am stuck on in a practice test.
The question is $$\frac{5^{2011} - 5^{2009} +24}{ 5^{2009} +1}$$
Can you cancel out the $5^{2009}$ or not?
 [/INST] $\dfrac{5^{2011}-5^{2009}+24}{5^{2009}+1}=$
$\dfrac{5^{2009+2}-5^{2009}+24}{5^{2009}+1}=$
$\dfrac{5^{2009}\cdot5^{2}-5^{2009}+24}{5^{2009}+1}=$
$\dfrac{5^{2009}\cdot25-5^{2009}+24}{5^{2009}+1}=$
$\dfrac{5^{2009}\cdot(25-1)+24}{5^{2009}+1}=$
$\dfrac{5^{2009}\cdot24+24}{5^{2009}+1}=$
$\dfrac{24\cdot(5^{2009}+1)}{5^{2009}+1}=$
$24\cdot\dfrac{5^{2009}+1}{5^{2009}+1}=$
$24$
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