Question 86197: (3 over x-5)+1 divided by 1- (4 over x-5)
I hope this makes sense. Thanks for any help you can offer. I'm stuck on this one. Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! (3 over x-5)+1 divided by 1- (4 over x-5)
: + 1
--------------
1 -
:
simplify the numerator: = =
:
Simplify the denominator: = =
:
Invert the denominator and multiply: * = ; canceled the (x-5)'s
:
Did this help
---------------------------------------------------------------------
Route 2:
Start with the given expression
Convert each "1" into
Combine the fractions
Multiply the fractions by flipping the 2nd fraction
Notice these terms cancel
Now combine like terms
which looks just like the original answer.
So no matter what route you take, the expression
simplifies to
Check:
One way we could verify this is to graph both expressions as equations like this
Graph the first equation (just set the expression equal to y)
graph of
Now graph the 2nd equation graph of
Notice how they trace out the same path. If they were plotted on the same graph, one would overlap another perfectly. This means they are equivalent (minus the discontinuous hole) and this verifies our answer.