Cancelling Algebraic FractionsDate: 11/11/2002 at 07:17:15 From: Dean James Subject: Algebraic fractions I am currently doing some last day revision for my maths GCSE (Higher Tier), which I will be taking over this week. I have looked through all of my study materials, but I still don't understand how to cancel down algebraic fractions, as they don't explain it very thoroughly. Could you please explain? Thanking you in anticipation, Dean James Date: 11/11/2002 at 10:19:39 From: Doctor Ian Subject: Re: Algebraic fractions Hi Dean, It's basically the same idea as reducing other kinds of fractions using prime factors. For example, here's how to do it using only numbers: 72 2 * 2 * 2 * 3 * 3 2 2 3 2 * 3 -- = ---------------------- = - * - * - * ----- = 6/5 60 2 * 2 * 3 * 5 2 2 3 5 You can do exactly the same thing using variables as your 'prime factors': x^3 y^4 z x * x * x * y * y * y * y * z ----------- = ----------------------------------------- x y^2 z^4 x * y * y * z * z * z * z x * x * y * y = ------------- z * z * z x^2 y^2 = ------- z^3 Eventually, as you get more practice with this, you'll notice that you can accomplish the same thing just by subtracting exponents: x^3 y^4 z ----------- = x^(3-1) y^(4-2) z^(1-4) = x^2 y^2 z^-3 x y^2 z^4 The other kind of cancellation that often occurs requires you to factor polynomials, e.g., x^2 + 3x + 2 (x+1)(x+2) (x+1) (x+2) ------------ = ---------- = ----- * ----- = (x+2)/(x-1) x^2 - 1 (x+1)(x-1) (x+1) (x-1) But it's all really the same thing: Break the numerator and denominator into the most basic possible factors; and eliminate any factor that appears in both the numerator and the denominator. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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