Question

Simplify the rational expression. State any restrictions on the variable.
n^4-11n^2+30/n^4-7n^2+10

Answer 1

\[\frac{ n^{4}-11n^{2}+30 }{n^{4}-7n ^{2}+10 }\]

Answer 2

did you try to factor?

Answer 3

idk how to

Answer 4

Are you familiar with AC method of factoring?

Answer 5

nope :/

Answer 6

AC method is mostly used for factoring quadratic expressions. But in this special case, both the numerator and denominator are very similar to quadratic expressions. So the method is can be applied.

Just pretend x^2 = u, then you have,
u^2 - 11u + 30,

do you see what I did there?

Answer 7

ohh. yes i see

Answer 8

ok, now it's just the matter of factoring u^2 - 11u + 30 using AC method.

Recall that the general quadratic equations is
Ax^2 + Bx + C.

But for sake of matching variables, I'm going to change it to
Au^2 + Bu + C

Ok so far?

Answer 9

ive got this so far...i did n^2=t
so..

Answer 10

\[\frac{ t^{2}-11t+30 }{ t^{2}-7t+10 }\]

Answer 11

then...

Answer 12

\[\frac{ (t-5)(t-6) }{ (t-2)(t-5) }\]

Answer 13

(^-^)b good job. Save me time haha. Now do you see anything canceling?

Answer 14

\[\frac{ n^{2} -6}{ n^{2}-2}\]

Answer 15

now i just need to figure out the restrictions

Answer 16

well, can you divide by 0?

Answer 17

no?

Answer 18

right. What does that tell you about the denominator?

Answer 19

idk >_< im lost again

Answer 20

can denominator be 0?