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

AlexandraMarie112

## Homework Statement

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

## 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.

Mentor

## Homework Statement

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

## 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 x5/2.

AlexandraMarie112
Mentor
2022 Award
What happens, if you simply divide by / cancel x?