Algebraic Fractions help?!?

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In general, to simply these types of problems, you factor the numerator and denominator and then reduce by canceling like factors.

        x² - 4            ← Notice that this is the difference of squares x²-2²

   —————

    x² - 5x + 6

     (x-2)(x+2)

= —————            ← Now, cancel the (x-2)'s

     (x-3)(x-2)

      x + 2

= ————            ← ANSWER

      x - 3

Have a good one!

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x^2 - 4 is the difference of two squares;

it's equal to (x + 2)(x - 2)

x^2 - 5x + 6 is a factorable quadratic:

it's equal to (x - 2)(x - 3).

So now we can write the fraction as

(x + 2)(x - 2)/((x - 2)(x - 3).

WE can cancel x - 2, and get

(x + 2)/(x - 3)

x^2 - 4 / x^2 - 5x + 6

Do you know how to factor?

http://www.purplemath.com/modules/factquad.htm

(x-2)(x+2)/(x-2)(x-3) Cancel (x-2)'s

(x+2)/(x-3)

That was so simple, right?

= 1/x^2(x^4 - 4 - 5x^3 + 6x^2)

= (x^4 - 5x^3 + 6x^2 - 4)/x^2