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## Multiply Rationals Expression and Functions

Multiply Rational Expression

(1)

x^2-6x          x^2-6x-16
-----------   .   ---------------
x^2+2x-80      x^2-8x+12

(2)

x^2+12x+20     x^2-x-56
----------------  . --------------
x^2-13x+40     x^2+18x+90

(3)

x^2+6x-55     x^3+216
------------- . --------------
x^2+6x       x^2-9x+20

(4)

2x^2+24x+22      x^2+3x-10
....................  .  .................
8x^2+104x+320   x^2+7x+6

For the given functions f(x), find f(g).g(x)

x^2-9x+20             x^2+6x-16
f(x) =  ............... ,g(x) = --------------
x^2+x-2                x^2-25

x^2+3x-28
f(x)=x+7,g(x)= ....................
x^2+14x+49

factor the terms of each fraction and simplify before you multiply
cross out each common factor that exists in a numerator and in a denominator

1)       (x)(x-6)        (x-8)(x+2)        (x)(x+2)
__________  .  __________ =  _________

(x+10)(x-8)      (x-6)(x-2)        (x+10)(x-2)

2) I am assuming a typo in #2

(x+10)(x+2)      (x-8)(x+7)       (x+2)(x+7)
___________  .  __________ =  __________

(x-8)(x-5)         (x+8)(x+10)     (x-5)(x+8)

3)   (x+11)(x-5)       (x+6)(x^2-6x+36)       (x+11)(x^2-6x+36)
__________  .   ________________ =   ________________

(x)(x+6)            (x-5)(x-4)                    (x)(x-4)

4)   (2)(x+11)(x+1)       (x+5)(x-2)         (x+11)(x-2)
______________  .  __________  =  ___________

(8)(x+8)(x+5)         (x+1)(x+6)       (4)(x+8)(x+6)

I assume you mean f(x)*g(x)

(x-5)(x-4)       (x+8)(x-2)       (x-4)(x+8)(x-2)
_________  .  _________  =  _____________

(x+2)(x-1)     (x-5)(x+5)       (x+2)(x-1)(x+5)

(x+7)(x-4)
(x+7) .  __________  =  (x-4)

(x+7)(x+7)