SOLUTION: simplify 3 over x-5 +1(the 1 is on the outer right) over 1 is on the outer left -4 over x-5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: simplify 3 over x-5 +1(the 1 is on the outer right) over 1 is on the outer left -4 over x-5      Log On


   

Question 86922: simplify
3
over
x-5
+1(the 1 is on the outer right)
over
1 is on the outer left
-4
over
x-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2F%28x-5%29%2B1%29%2F%281-4%2F%28x-5%29%29 Start with the given expression

%283%2F%28x-5%29%2B%28x-5%29%2F%28x-5%29%29%2F%28%28x-5%29%2F%28x-5%29-4%2F%28x-5%29%29 Convert each "1" into %28x-5%29%2F%28x-5%29

%28%283%2Bx-5%29%2F%28x-5%29%29%2F%28%28x-5-4%29%2F%28x-5%29%29 Combine the fractions

%28%283%2Bx-5%29%2F%28x-5%29%29%2A%28%28x-5%29%2F%28x-5-4%29%29 Multiply the fractions by flipping the 2nd fraction

%28%283%2Bx-5%29%2Fcross%28%28x-5%29%29%29%2A%28cross%28%28x-5%29%29%2F%28x-5-4%29%29 Notice these terms cancel

%283%2Bx-5%29%2F%28x-5-4%29

Now combine like terms

%28x-2%29%2F%28x-9%29


So the expression

%283%2F%28x-5%29%2B1%29%2F%281-4%2F%28x-5%29%29

simplifies to

%28x-2%29%2F%28x-9%29


Check:
One way we could verify this is to graph both expressions as equations like this

Graph the first equation y=%283%2F%28x-5%29%2B1%29%2F%281-4%2F%28x-5%29%29 (just set the expression equal to y)
graph of y=%283%2F%28x-5%29%2B1%29%2F%281-4%2F%28x-5%29%29

Now graph the 2nd equation y=%28x-2%29%2F%28x-9%29
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28x-2%29%2F%28x-9%29%29+ graph of y=%28x-2%29%2F%28x-9%29

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.