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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

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

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