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Add or subtract this rational expressions.


Add or subtract this rational expressions.

(1)

          10                7
--------------- + ------------
x^2-16x+60       x^2-100


(2)

        3                         2
....................  -    ...............
x^2-6x-16x           x^2-2x-48
Add or subtract this rational expressions.

              (1)

          10                7
--------------- + ------------
x^2-16x+60       x^2-100


                  (2)

        3                   2
.................... -  ...............
x^2-6x-16x        x^2-2x-48

Comments

Ibadan,
 
I seem to recall having done these a few days ago.
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1 Answer

1.
 
         10                    7
--------------- + ------------ =
x^2-16x+60         x^2-100
 
[10/(x2 -16x + 60)] + [7/(x2 - 100)]
 
Multiply both fractions by (x2 - 16x + 60)*(x2 - 100) to create a common denominator:
 
[10* (x2 - 100) + 7*(x2 - 16x +60)]/[(x2 - 100)*(x2 - 16x + 60)]
 
Factor
 
[10*(x + 10)*(x - 10) + 7*(x - 10)*(x - 6)]/[(x - 10)2*(x + 10)*(x - 6)] =
 
[10*(x + 10) + 7*(x - 6)]/[(x - 10)(x + 10)*(x - 6)] =
 
(10*x + 100 + 7x - 42)/[(x - 10)(x + 10)*(x - 6)] =
 
(17x +58)/[(x - 10)(x + 10)*(x - 6)]
 
No. 2 can be solved by the same method.
 
          3                    2
.................... - ...............
x^2-6x-16x      x^2-2x-48
 
 
I am assuming you meant to type x^2 - 6x - 16 instead of x^2-6x-16x 
 
3*(x2 - 2x - 48)*(x2 - 6x - 16) - 2*(x2 - 2x - 48)*(x2 - 6x - 16)
_____________________________________________________
 
                   (x2 - 2x - 48)*(x2 - 6x - 16)
 
Factor
 
3*[(x - 8)*(x + 6)*(x - 8)*(x + 2)] + 2*[(x - 8)*(x + 6)*(x - 8)*(x + 2)]
__________________________________________________________    =
                             [(x - 8)*(x + 6)*(x - 8)*(x + 2)]
 
 
(x + 14)/[(x - 8)*(x + 2)*(x + 6)