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Rational Expression and Equations ,COMPLEX RATIONAL EXPRESSION

Simplify the given rational expression.

      (1)

     11     18
1- ---- + ------
      x     x^2
--------------------
      2        63
1- ---- - --------
      x        x^2


       (2)

     5
x+----
     8
----------
     7
x - ---
      2


   (3)

      8
10+---
      x
----------
      20
25+----
       x
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1 Answer

1.  1 - (11/x) + (18x2)
     _______________
     1 - (2/x) - (63/x2)
 
Rewrite the numerator as [(x2 - 11x + 18)/x2]  and the denominator as [(x2 - 2x - 63)/x2]
 
Factor the numerator as {[(x - 9)(x - 2)]/x2} and the denominator as {[(x - 9)(x + 7)]/x2}
 
Multiply the numerator by the reciprocal of the denominator:
 
{[(x - 9)(x - 2)]/x2} * {x2/[(x - 9)(x + 7)]} = (x - 2)/(x + 7)
 
2. [x + (5/8)]/[x - (7/2)] = [(8x + 5)/8]/[(2x - 7)/2] = [(8x + 5)/8]*[2/(2x + 7)]
 
= (8x + 5)/[4(2x - 7)]
 
3.  [10 + (8/x)]/[25 + (20/x)] = [(10x + 8]/x]/[(25x + 20)/x] =  [(10x + 8]/x]*[x/(25x + 20)]
 
= (10x + 8)/(25x + 20) = [2(5x + 4)]/[5(5x + 4)]  = (2/5)