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How do you simplify the expression #(1/(t-1)+1/(t+1))/(1/t-1/t^2)#?

Answer 1

Kennedy Adams

# (2t^3)/{(t-1)^2(t+1)}#.

We have, #"The Nr."=1/(t-1)+1/(t+1)#,

#={(t+1)+(t-1)}/{(t-1)(t+1)}#,

#:." The Nr."=(2t)/{(t-1)(t+1)}#.

#"The Dr."=1/t-1/t^2#,

#=(t-1)/t^2#.

#:." The Exp."=(2t)/{(t-1)(t+1)}-:(t-1)/t^2#,

#=(2t)/{(t-1)(t+1)}xxt^2/(t-1)#,

#=(2t^3)/{(t-1)^2(t+1)}#.

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Answer 2

Jace Anderson

To simplify the expression (1/(t-1)+1/(t+1))/(1/t-1/t^2), we can follow these steps:

Find a common denominator for the fractions in the numerator: (t-1)(t+1).
Rewrite the fractions in the numerator with the common denominator: (t+1)/(t-1)(t+1) + (t-1)/(t-1)(t+1).
Combine the fractions in the numerator: (t+1 + t-1)/(t-1)(t+1).
Simplify the numerator: (2t)/(t-1)(t+1).
Invert the denominator and multiply: (2t)*(t^2)/(t-1).
Simplify the expression: 2t^3/(t-1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.