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First, you need to put the numerator and denominator within brackets, such as:
`((a^2 - 1))/((a^2 + 2a - 3))`
We notice that the numerator is a difference of two squares that returns the special product:
`a^2 - 1 = (a-1)(a+1)`
We'll decompose the denominator in it's factors. For this reason, we'll apply the quadratic formula, to determine the roots of the expression from denominator.
a1 = (-2+`sqrt(4 + 12)` )/2
a1 = (-2+4)/2
a1 = 1
a2 = (-2-4)/2
a2 = -3
The denominator could be written as a product of linear factors:
`a^2 + 2a - 3 = (a - 1)(a + 3)`
We'll re-write the given expression:
`((a^2 - 1))/((a^2 + 2a - 3))` = `[(a-1)(a+1)]/[(a-1)(a+3)]`
We'll reduce the fraction and we'll get:
`((a^2 - 1))/((a^2 + 2a - 3)) = ((a + 1))/((a+3))`
Posted by giorgiana1976 on August 25, 2011 at 9:13 PM (Answer #1)
High School Teacher
Factor the numerator using the difference of two squares:
Factor the denominator. Here were are looking for values that ADD to = -3 and MULTIPLY to = +2. We can use +3 and -1.
Rewrite the orginal fraction with the factored numerator and denominator
(a+1)(a-1) / (a+3)(a-1)
Cancel out the like terms (a-1) , we are left with
(a+1) / (a+3)
Posted by mathematicianmckenna on August 28, 2011 at 6:43 AM (Answer #2)
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