Question
Todd incorrectly argues that since$$\frac{a^{2}-4}{a-2}=\frac{a^{2}}{a}+\frac{-4}{-2}=a+2$$is correct, it follows that$$\frac{x^{2}+9}{x+1}=\frac{x^{2}}{x}+\frac{9}{1}=x+9$$Explain his misconception.
Step 1
The correct way to simplify the left side of the equation is to factor the numerator as follows: $$ \frac{a^{2}-4}{a-2}=\frac{(a-2)(a+2)}{a-2}=a+2 $$ So, Todd's first equation is correct, but his method of simplification is incorrect. Show more…
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