SOLUTION: This is a complex fraction. Instructions are to simplify. {{{2+3/(1+2/(1-x))}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: This is a complex fraction. Instructions are to simplify. {{{2+3/(1+2/(1-x))}}}       Log On


   



Question 143734: This is a complex fraction. Instructions are to simplify.

2%2B3%2F%281%2B2%2F%281-x%29%29

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
      
2%2B3%2F%281%2B2%2F%281-x%29%29

First do only the part boxed in

2%2B3%2F%28highlight%281%2B2%2F%281-x%29%29%29

1%2B2%2F%281-x%29

Write 1 as 1%2F1

1%2F1%2B2%2F%281-x%29

Get the LCD of 1-x.  Multiply top and
bottom of 1%2F1 by %281-x%29%29

%281%281-x%29%29%2F%281%281-x%29%29%2B2%2F%281-x%29

%281-x%29%2F%281-x%29+%2B+2%2F%281-x%29+

Combine the numerators over the LCD:

%281-x%2B2%29%2F%281-x%29

%283-x%29%2F%281-x%29

Now go back to 
2%2B3%2F%28highlight%281%2B2%2F%281-x%29%29%29

and replace the boxed-in part by %283-x%29%2F%281-x%29

2%2B3%2Fhighlight%28+%283-x%29%2F%281-x%29%29+

Erasing the box:

2%2B3%2F%28+%283-x%29%2F%281-x%29%29+

Now do only the part boxed in here:

2%2Bhighlight%283%2F%28+%283-x%29%2F%281-x%29%29%29+

3%2F%28+%283-x%29%2F%281-x%29%29+

This can be done by inverting and multiplying:

3%2A+%28%281-x%29%2F%283-x%29%29+

Write 3 as %283%2F1%29:

%283%2F1%29%2A+%28%281-x%29%2F%283-x%29%29+

Multiply numerators and denominators:

%283-3x%29%2F%283-x%29+

Now go back to

2%2Bhighlight%283%2F%28+%283-x%29%2F%281-x%29%29%29+

and replace the boxed-in part by %283-3x%29%2F%283-x%29

2%2Bhighlight%28+%283-3x%29%2F%283-x%29++%29+

Erasing the box:

2%2B+%283-3x%29%2F%283-x%29+++

Write 2 as 2%2F1

2%2F1%2B%283-3x%29%2F%283-x%29

Get the LCD of 3-x.  Multiply top and
bottom of 2%2F1 by %283-x%29

%282%283-x%29%29%2F%281%283-x%29%29%2B%283-3x%29%2F%283-x%29

%286-2x%29%2F%283-x%29+%2B+%283-3x%29%2F%283-x%29+

Combine the numerators over the LCD:

%286-2x%2B3-3x%29%2F%283-x%29

%289-5x%29%2F%283-x%29

Edwin