Question 346907: how do I simplify a ratio of polynomials: Problem 1
u^2 - 7u + 12/ 4u^2 -36u +72
I have been working on these all day.
thank you Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! I assume your fraction is:
If so, please put multiple term numerators and denominators, like these, in parentheses when posting your questions. Tutors are less likely to answer questions that are not clear.
To simplify/reduce any fraction you look for common factors of both the numerator and denominator. In other words you are looking for expressions which will divide evenly into both the numerator and denominator.
So we have to factor the numerator and denominator (and hope we find common factors). How easy or hard you find reducing these fractions is determined in large part by how good you are at factoring.
Your numerator is a trinomial that factors fairly easily. You look for factors of 12 that add up to -7. With a little thought and remembering that positive 12 can have two negative factors, too, we should find that -4 and -3 have a product of 12 and a sum of -7. So the numerator factors into (u-4)(u-3).
In the denominator we start with the Greatest Common Factor (GCF). The GCF of you denominator is 4. So ths initial factored form of your denominator is: . The second factor of the denominator is a trinomal which factors in the same way the numerator did. We look for factors of 18 that add up to -9. This time we find that -3 and -6 have a product of 18 and a sum of -9. So the final factored form of the denominator is: 4(u-3)(u-6)
Our fraction in factored form is:
We can now see that there is a common factor: (u-3). We can cancel this common factor:
leaving:
Nothing else cancels so we just multiply out the denominator:
This is the reduced/simplified fraction.
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