SOLUTION: complex rational expressions 1/5 - 1/y __________ 5-y/5

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Question 198578: complex rational expressions

1/5 - 1/y
__________
5-y/5
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the expression %281%2F5-1%2Fy%29%2F%285-y%2F5%29???


%281%2F5-1%2Fy%29%2F%285-y%2F5%29 Start with the given expression.


Multiply EVERY term by the inner LCD 5y to clear out the inner fractions.


%281%2Ay-1%2A5%29%2F%285%2A5y-y%2Ay%29 Simplify


%28y-5%29%2F%2825y-y%5E2%29 Multiply



So %281%2F5-1%2Fy%29%2F%285-y%2F5%29=%28y-5%29%2F%2825y-y%5E2%29


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OR...

Is the expression %281%2F5-1%2Fy%29%2F%28%285-y%29%2F5%29 ???



%281%2F5-1%2Fy%29%2F%28%285-y%29%2F5%29 Start with the given expression.


Multiply EVERY term by the inner LCD 5y to clear out the inner fractions.


%281%2Ay-1%2A5%29%2F%28y%285-y%29%29 Simplify


%28y-5%29%2F%28y%285-y%29%29 Multiply


%28y-5%29%2F%28-y%28y-5%29%29 Factor the denominator


-%28y-5%29%2F%28y%28y-5%29%29 Reduce


-cross%28%28y-5%29%29%2F%28y%2Across%28%28y-5%29%29%29 Cancel out the common terms.


-1%2Fy Simplify


So %281%2F5-1%2Fy%29%2F%28%285-y%29%2F5%29=-1%2Fy

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1/5 - 1/y
__________
5-y/5
=======================
[(y-5)/(5y)] / [(25-y)/5]
-----
Invert the denominator and multiply to get:
= [(y-5)/(5y)] * [5/(25-y)]
------
Cancel the "5" factor to get:
= (y-5)/(y(25-y))
======================
Cheers,
Stan H.