Algebra help!?

x^2 - 4/x^2 - x -2 divided by x+2/x-2

do you mean ... (x^2 - 4)/(x^2 - x -2) divided by (x+2)/(x-2) ???

= [(x + 2)(x - 2) / ((x - 2)(x+1)) ] X [(x-2) / (x+2)] ... cap X is multiplication symbol ... now cancel

= (x - 2) / (x + 1) << answer

You should clarify what you are asking with parentheses. I am going to assume that you mean:

[ (x^2 - 4) / (x^2 - x - 2) ] / [ (x + 2) / (x - 2) ]

If that is the case, then the first thing I would do is factor both (x^2 - 4) and (x^2 - x - 2):

(x^2 - 4)

(x^2 + 0x - 4)

-------------------

(x + 2)(x - 2)

(x^2 - x - 2)

(x^2 - 1x - 2)

-------------------

(x + 1)(x - 2)

Now you have:

[ (x+2)(x-2) / (x+1)(x-2) ] / [ (x+2) / (x-2) ]

or

[ (x + 2) / (x + 1) ] / [ (x + 2) / (x - 2) ]

Diving a fraction by another number is the same as multiplying the numerator by the reciprocal of the denominator:

[ (x + 2) / (x + 1) ] / [ (x + 2) / (x - 2) ]

[ (x + 2) / (x + 1) ] * [ (x - 2) / (x + 2) ]

(x + 2)(x - 2) / (x + 1)( x + 2)

-------------------------------------------

(x - 2) / (x + 1)

The answer to your problem is (x - 2) / (x + 1)

factor what you can !

x^2 - 4 = (x + 2)(x - 2)

x^2 - x - 2 = (x - 2)(x + 1)

now...multiply...

[(x + 2)(x - 2)]/[(x - 2)(x + 1)] * (x - 2)/(x + 2) = (x - 2) / (x + 1)

Ω