Rational Equation Review

Express the rational fraction in lowest term:
y² + 2y - 15
-----------------
y² + 4y - 21

• 2y - 15
  ------------
  4y - 21
• 2y - 5
  ------------
  4y - 7
• y + 5
  ------------
  y + 7
• y² + 2y - 15
  -----------------
  y² + 4y - 21

Write the rational expression in lowest terms:
6 - m
--------
m - 6

• 1
• -1
• -m
• already in lowest terms

   Perform the indicated operation and express in lowest terms:
 3p - 3          6p²
----------  *   -------
    p             4p - 4

• 9p
  ----
  2
• 12p² + 24p + 12
  -----------------------
           6p³
• 18p³ - 18p^{2
  -----------------}
  4p² - 4p
  
• 2
  ---
  9p

Perform the indicated operation and express in lowest terms:
x²  + 9x  + 14         x² + 2x 
------------------    /   ------------  
x² + 16x + 63           x² + 6x - 27

• x - 3
  --------
  x
• x - 3
• x
  --------------------
  x² + 16x + 63
• x - 3
  -------------
  x² + 9x

Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared aspotential solutions.
     9                  1                         1        
----------   +   ----     =        ----------
6x + 13           x                13x - 9

• 0,   -13 ,   9 
           ----   ---
             6    13
• -13 ,   9 
    ----   ---
       6    13
• 0,    13 ,  -9 
           ----   ---
             6    13
• -13 ,   9, -9 
  -----   ---      
       6    13        

Solve the equation:
2         10               -80
----- +  ----  =    ---------
x - 8      x         x² - 8x

• {0}
• No solution
• {0, 8}
• { -8 }

Solve the equation:
1        1        6
       +  --- = --- 
            x        x²

• {2, 3}
• {-3, -2}
• {-2, 3}
• {-3, 2}

Simplify the complex fraction:
1/a + 1
-----------
1/a - 1

• 1 + a
  --------
  1 - a
• a
  --------
  1 - a²
• 1
• 1 - a²

Simplify the complex fraction:
4 + 2/x
------------
x/4 + 1/8

• 1
• 16
• 16
  -----
  x
• x
  -----
  16