(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

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)

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

Tutors, sign in to answer this question.

1. 1 - (11/x) + (18x^{2})

_______________

1 - (2/x) - (63/x^{2})

Rewrite the numerator as [(x^{2} - 11x + 18)/x^{2}] and the denominator as [(x^{2} - 2x - 63)/x^{2}]

Factor the numerator as {[(x - 9)(x - 2)]/x^{2}} and the denominator as {[(x - 9)(x + 7)]/x^{2}}

Multiply the numerator by the reciprocal of the denominator:

{[(x - 9)(x - 2)]/x^{2}} * {x^{2}/[(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**)

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