<s>[INST] Reducing a fraction in algebra? How would I reduce the following fraction?
$$\frac{4A^2-B^2}{4A^2-4AB+B^2}$$
I am not sure how I would reduce it.
 [/INST] The numerator is a difference of squares, so it factors:
$$4A^2 - B^2 = (2A)^2 - B^2= (2A-B)(2A+B).$$
The denominator is a perfect square:
$$4A^2 - 4AB + B^2 = (2A)^2 - 2(2A)B + B^2 = (2A-B)^2.$$
Then you can cancel one factor:
$$\frac{4A^2 - B^2}{4A^2 - 4AB+B^2} = \frac{(2A-B)(2A+B)}{(2A-B)^2} = \frac{2A+B}{2A-B}.$$
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