Order of Operations Explained
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Explain how subtracting [4w/(w^2-8w+150]-[6/w-3)] is similar and different to subtracting 4/5 - 2/15. Show all steps in both addition problems.
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Solution Summary
Order of operations are investigated in this solution.
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Taking the first subtraction:
4w 6
------------ - ---
w^2 - 8w + 15 w - 3
We can notice that (w-3) is a factor of the quadratic denominator on the left (* see end for explanation of this.)
= 4w 6
---------- - ---
(w - 3)(w - 5) w - 3
We can multiply the right hand term by (w - 5)/(w - 5) = 1 without altering it:
= 4w 6 (w - 5)
---------- - ...
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