SOLUTION: Hello, Kindly ask someone to help me with the following problem. Study the function and represent it graphically: {{{f(x)=(x)/(x-1)+(1)/(x+1)-x-(1)/(3)}}} Thank you very m

SOLUTION: Hello, Kindly ask someone to help me with the following problem. Study the function and represent it graphically: {{{f(x)=(x)/(x-1)+(1)/(x+1)-x-(1)/(3)}}} Thank you very m

Algebra.Com

Question 1117633: Hello,
Kindly ask someone to help me with the following problem.
Study the function and represent it graphically:
Thank you very much!

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

Note that the function will have vertical asymptotes at

and

. As the independent variable approaches -1 from the left, the value of the function will be a large negative number, and from the right, a large positive. Approaching 1 from the left is also a large negative, and from the right, a large positive.

Evaluating

we get

Applying the common denominator of

and adding all of the fractions (verification of this step left as an exercise for the student), we simplify to:

So we note that as

increases and decreases without bound, the function begins to behave very much like

.

John

My calculator said it, I believe it, that settles it

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