Limits...what am I doing wrong ? (Without hopital)

[AlexandraMarie112]

Homework Statement

Limx--->positive infinity sqrt(3x^5-2x) - sqrt(3x^5-7x)

Homework Equations

The Attempt at a Solution

The first thing I did was rationalize. I got (5x)/ [ sqrt(3x^5-2x) + sqrt(3x^5-7x)]. Then I divided the top and bottom by x^5 but this is where I feel like I am doing something wrong. But I don't know what. Am I even supposed to divide by x^5 ? Because the other problems I've solved so far have been with an x^2.

 

[Mark44]

Homework Statement

Limx--->positive infinity sqrt(3x^5-2x) - sqrt(3x^5-7x)

Homework Equations

The Attempt at a Solution

The first thing I did was rationalize. I got (5x)/ [ sqrt(3x^5-2x) + sqrt(3x^5-7x)]. Then I divided the top and bottom by x^5 but this is where I feel like I am doing something wrong. But I don't know what. Am I even supposed to divide by x^5 ? Because the other problems I've solved so far have been with an x^2.

Factor x⁵ out of each radical, and bring each out of its radical as x^5/2.

 

[fresh_42]

What happens, if you simply divide by / cancel x?