Question

Reduction
(x^2-s^2)^3 / (x-s)^4
(grateful for help!:))

Answer 1

the first thing is remember x^2-s^2 can be factored (memorize this!)
into (x-s)(x+s)

that means your problem is
\[ \frac{( (x-s)(x+s))^3}{(x-s)^4} \]
can you finish?

Answer 2

in ^2??
i get it as:
((x-s)(x+s))^3/(x-s)^4
'cause.: (ab)^n = a^n * b^n it becomes:
((x-s)(x+s))^3 = (x-s)^3 * (x+s)^3
(x-s)^3 * (x+s)^3 / (x-s)^4
n > m
= ( x + s ) ^ 3 / ( x - s ) ^ ( 4 - 3 )
= (x+s)^3/(x-s)

or am I totally wrong?

Answer 3

you are totally correct

Answer 4

btw, your rule n>m comes from this.
if you had
\[\frac{x^3}{x^4} = \frac{x\cdot x\cdot x}{x\cdot x\cdot x \cdot x}\]
of course you can write that as
\[ \frac{x}{x} \cdot \frac{x}{x} \cdot \frac{x}{x} \cdot \frac{1}{x} \]
\( \frac{x}{x} \) is 1, so that all simplifies to
\[ 1\cdot 1\cdot 1 \cdot \frac{1}{x}= \frac{1}{x} \]

Answer 5

alright, i see! thank you for your help =D