SOLUTION: (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.

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
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
There are many ways to solve this problem, here are two routes you could take:

Route 1:

Start with the given expression

Let

Multiply the expression by (which is a form of 1)

Distribute

Multiply and simplify

Replace y with

Combine like terms

---------------------------------------------------------------------
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.

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