Aim: How do we solve complex fraction?

Aim: How do we solve complex fraction?

Complex Fraction: An expression in which the denominator or numerator, or they both contain fractions. 

To solve complex fraction, you should always solve the numerator and denominator expressions one at a time to make the complex fraction into one single fraction expression.  

Example: 
(1/x)-1
x-(1/x)

1)Simplify the numerator expression.
1-x
  x    

2) Simplify the denominator expression.
x^2-1
   x         

3) You have the single fraction

1-x             x^2-1
   x       ÷     x 

4) Do keep change flip.

1-x           x        
  x   *    x^2-1

5) Factor 1-x and x^2-1.
-1(x-1)   *        x        
    x            (x+1)(x-1)


6)Simplify

-1(x-1)   *        x   1         
    x           (x+1)(x-1)  1

7) Answer
     -1     

 (x+1)     



Source:
http://www.www-mathtutor.com/simplifying-complex-fractions-1.html

How do we use inverse variation?

Aim: How do we use inverse variation?

Inverse Variation is a relationship between two variables x and y, where x varies inversely with y and their product is constant. In other words, when x increases, y decreases by the same factor to 
make sure the product remains the same. 

x*y=k  ( K is constant)

We can find K by multiplying x and y.

Example:

1. If x=4 and y=5, write an equation that describing this inverse variation?
Multiply x and y
4*5=20
xy=20 or y=20/x

2. Find y using inverse variation?

x	y
3	20
6	10
12	y

First, multiply 3 and 20 to find the constant product.
20*3=60
xy=60 (The product of x and y will always be 60)
Then, substitute 12 for x.
12y=60
Now, divide 12 from both side to get the y alone. 
12y=60
12    12
The answer is y=5.