Limit Calc: Find $\lim\limits_{t\to -1} \frac{\sqrt[3]{t}+1}{\sqrt[5]{t}+1}

[nuuskur]

Homework Statement

Find the limit \lim\limits_{t\to -1}\frac{\sqrt[3]{t}+1}{\sqrt[5]{t}+1}. Needless to say: No L'Hopital's rule, otherwise this thread would not exist.

Homework Equations

The Attempt at a Solution

Have tried multiplying the fraction such that I get the difference of squares in denominator - no avail.
This is analysis 1 course material .. *blushes*

There is something I have forgotten about, this is supposed to be a really easy problem.
Hints, anyone?

 

[Ray Vickson]

Homework Statement

Find the limit \lim\limits_{t\to -1}\frac{\sqrt[3]{t}+1}{\sqrt[5]{t}+1}. Needless to say: No L'Hopital's rule, otherwise this thread would not exist.

Homework Equations

The Attempt at a Solution

Have tried multiplying the fraction such that I get the difference of squares in denominator - no avail.
This is analysis 1 course material .. *blushes*

There is something I have forgotten about, this is supposed to be a really easy problem.
Hints, anyone?

Did somebody forbid you from using l'Hospital's rule?

 

[Mark44]

Have tried multiplying the fraction such that I get the difference of squares in denominator - no avail.

Of course that won't work -- neither radical contains a square root.

What will work is to multiply each of the numerator and denominator by 1, in a suitable form.

Hint 1: $(a + b)(a^2 - ab + b^2) = a^3 + b^3$
Hint 2: $(a + b)(a^4 -a^3b + a^2b^2 - ab^3 + b^4) = a^5 + b^5$