SOLUTION: simplify: y-z/a+b times a^2-b^2/z-y please do it step by step so I understand it

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Question 40707: simplify:
y-z/a+b times a^2-b^2/z-y
please do it step by step so I understand it
Answer by junior403(76) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify.
%28%28y-z%29%2F%28a%2Bb%29%29%2A%28%28a%5E2-b%5E2%29%2F%28z-y%29%29
First we need to simplify by factoring in order to cancel these expressions.
The numerator in the fraction on the right is the difference of two squares.
a%5E2+-+b%5E2
We can factor this as (a+b)(a-b)because if we FOIL these out we get a%5E2+-+b%5E2
In the denominator of the same fraction we can factor out a -1 in order to make the expression read (y-z) which is NOT the same as (z-y).
So now we have...
%28%28y-z%29%2F%28a%2Bb%29%29%2A%28%28a%2Bb%29%28a-b%29%2F-1%28y-z%29%29
Now we can cancel out all of our like terms.
(y-z) in the numerator of the first expression can cancel with (y-z) in the denominator of the second expression.
%28%280%29%2F%28a%2Bb%29%29%2A%28%28a%2Bb%29%28a-b%29%2F-1%29
(a+b)in the denominator of the first expression can cancel with (a+b) in the numerator of the second expression.
Which becomes...
%28a-b%29%2F-1
Or...
-(a-b)
or...
(-a+b)
or...
(b-a)
This is in its simplist form.
I hope I explained this thoroughly enough for you.
Good Luck!