We'll determine the roots of the numerators and
denominators of both fractions:
x^2 +8x +7 =
0
We notice that the sum of the roots is -8 and the product
is 7, then the roots are: x1 = -7 and x2 = -1
We can write
the quadratic as a product of linear factors:
x^2 +8x +7 =
(x+1)(x+7)
In the case of denominator of the 1st fraction,
we'll recognize the perfect square:
x^2 +6x +9 =
(x+3)^2
We'll find the roots of the numerator of the 2nd
fraction:
x^2 - 13x - 18 =
0
x1 = [13+sqrt(169+72)]/2
x1
= [13+sqrt(241)]/2
x2 =
[13-sqrt(241)]/2
x^2 - 13x - 18 = (x - 13/2 - sqrt241/2)(x
- 13/2 + sqrt241/2)
We'll determine the roots of the 2nd
denominator:
x^2 - 5x - 6 =
0
x1 = -1, x2 = 6
x^2 - 5x - 6
= (x-6)(x+1)
The product of fractions will
be:
(x+1)*(x+7)*(x - 13/2 - sqrt241/2)*(x - 13/2 +
sqrt241/2)/(x+3)^2*(x-6)*(x+1)
We'll simplify
and we'll get: (x+7)*(x^2 - 13x -
18)/(x+3)^2*(x-6)
No comments:
Post a Comment