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Order of Operations Explained

Explain how subtracting [4w/(w^2-8w+150]-[6/w-3)] is similar and different to substracting 4/5 - 2/15. Show all steps in both addition problems.

Solution Preview

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)
---------- - ...

Solution Summary

Order of Operations are investigated.

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