Math Is Fun Forum

Rose-Red

Member

Registered: 2006-01-05

Posts: 19

Simplification

Hello,

does anyone know how I could simplify this expression:

(ar - ar² + ar³ - a)/(r-1)

polylog

Member

Registered: 2006-09-28

Posts: 162

Re: Simplification

I assume a is a constant. First factor it out:

Now we need to factor the numerator.

Call it f(r) = r^3 - r^2 + r - 1

Try values of r such that f(r) = 0. Notice that f(1) = 0.

Thus, by the factor theorem, (r-1) is a factor of f(r).

To find the other factor, use polynomial long division.

I get the other factor as (r^2 + 1)

Thus, f(r) = (r - 1)(r^2 + 1)

Now we can write:

Rose-Red

Member

Registered: 2006-01-05

Posts: 19

Re: Simplification

Thanx mate, that's the answer I needed to get

Last edited by Rose-Red (2006-10-25 19:42:54)

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: Simplification

But the expression is NOT defined when r=1

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