What are the restrictions for 4/x+1/x^2=1/5x^2

The restrictions will be:

x ≠ 0;  

x² ≠ 0 ⇒  x ≠ 0 ;  

5x² ≠ 0 ⇒ x² ≠ 0 ⇒  x ≠ 0;

Step-by-step explanation:

As we know that

There are two genuine reasons why domains are restricted.

We cannot divide the expression by 0 as it would be undefined then.

We cannot take the square root of a negative number, as the result will not be a defined.

Considering the expression

As we can not put x = 0 in the denominator as it would make the expression undefined.

In other words, the certain values which make the denominator equal to zero for a rational expression will be restricted values.

Hence, the restrictions will be:

x ≠ 0;  

x² ≠ 0 ⇒  x ≠ 0 ;  

5x² ≠ 0 ⇒ x² ≠ 0 ⇒  x ≠ 0;