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Complex Fraction

Simplify Complex Fraction

  (1)

3       2
--- + ---
7       3
----------
16     2
--- - ---
21     7
 
 
  (2)
        
        8
10+--
      x
---------
      20
25+----
       x
 
  (3)
  
      9       18
 
1- --- + -------
     x       x^2
-----------------
      2      15
1+ --- - -------
      x      x^2
 
 
    (1)
 
 3      2
--- + ---
 7      3
----------
16    2
--- - ---
21     7
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1 Answer

1)  simplify the top by adding 3/7 + 2/3
 
the common denominator is 21, so it becomes 9/21 + 14/21 = 23/21.
 
 
Now, simplify the bottom by subtracting 16/21 - 2/7
 
the common denominator here is also 21, so this becomes 16/21 - 6/21 = 10/21.
 
The line that divides the top from the bottom means DIVISION. 
 
Thus, 23/21 ÷ 10/21
 
But remember that when you divide, you change to multiplication and "flip" the second fraction (it's called the reciprocal).
 
So, now you have 23/21  • 21/10 =   23/10  (the 21s cancel since one is on top and one is on the bottom)
 
the answer in proper form is 2 3/10

Comments

2)  This one is similar to the first one except now you have a common denominator of x for the top and x for the bottom.
 
The top becomes   10x + 8
                                 x
 
The bottom becomes    25x + 20
                                        x
 
When you divide (really multiply and flip the bottom fraction) it looks like this:
 
 
10x + 8     •           x   
    x                 25x +20
 
 
Thus, the answer is  10x + 8
                             25x + 20
For #3 just multiply EVERY term by x2 to get:
 
x2 - 9x +18
x2 + 2x - 15
 
Both the top and bottom can be factored:
 
(x - 6)(x - 3)
(x + 5)(x - 3)
 
the (x - 3)s cancel so the answer is:
 
x - 6
x + 5

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