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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

### 1 Answer by Expert Tutors

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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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)