SOLUTION: simplify the rational expression: x^3-2x^2+x-2/x-2 Thank you so much for the help!!

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Question 182573This question is from textbook
: simplify the rational expression:
x^3-2x^2+x-2/x-2
Thank you so much for the help!! This question is from textbook

Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
simplify the rational expression:
x^3-2x^2+x-2/x-2
Factor the 1st two and the last two terms separately:
[x^2(x-2) + (x-2)]/(x-2)

= [(x-2)(x^2+1)] / (x-2)
= x^2 + 1
=================
Cheers,
Stan H.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Before you do anything else, determine values of the variable that must be excluded. For a rational expression, set the denominator equal to zero and solve:

So, regardless of what the expression looks like after simplification, the value 2 must remain excluded.

Use Polynomial Long Division:

goes into times, so:

so

Change signs of subtrahend and add:

Bring down the

goes into times, so:

so

Change signs of subtrahend and add:

Bring down the -2:

goes into times, so:

Finally:

Since the remainder is zero, divides evenly. Therefore we can say:

John