// End script hiding -->
SOLUTION: Please solve: x^4 - 4x^3 + 3x / x^2 -1 I get x^2 - 4x + 1 - x + 2/x^2 - 1
Algebra
->
Polynomials-and-rational-expressions
-> SOLUTION: Please solve: x^4 - 4x^3 + 3x / x^2 -1 I get x^2 - 4x + 1 - x + 2/x^2 - 1
Log On
Ad:
Mathway
solves algebra homework problems with step-by-step help!
Algebra: Polynomials, rational expressions and equations
Section
Solvers
Solvers
Lessons
Lessons
Answers archive
Answers
Click here to see ALL problems on Polynomials-and-rational-expressions
Question 5057
:
Please solve:
x^4 - 4x^3 + 3x / x^2 -1
I get x^2 - 4x + 1 - x + 2/x^2 - 1
Answer by
rapaljer(4670)
(
Show Source
):
You can
put this solution on YOUR website!
First factor out the x from the numerator, and factor the denominator:
Now the trick is this: Is
divisible by either (x-1) or (x+1). It turns out (and it usually does!) that it is, in this case, divisible by (x-1). You will have to do synthetic or polynomial division (which I don't know how to do on this website!) as follows:
Divide:
1 | 1 -4 0 3
XXX 1 -3 -3
_____________________
XX 1 -3 -3 0
Other tutors could probably write it better, but basically, the remainder is zero, and the quotient is
Therefore the x-1 divides out leaving this:
By the way, the remaining trinomial does not factor.
R^2 at SCC