Shouldn’t have a difference.

x + 7
= 1/3 (3x + 21)
= 1/3 (3x + 5 + 16)

Then, (x + 7) / (3x + 5)
= 1/3 + 16/3 divided by (3x + 5)

16 / [3 (3x + 5)] will approach to zero but from the negative side.

3 (3x + 5) will become very negative number.

But 16 divided by a very large negative number will yield a number close to zero .

ahhh i made a carless mistake, i now understand, thank you so much!

Actually as a side point, dividing by x^2 fails in this scenario.

It runs into “four mini-fractions within a single large fraction” where all the terms in x lie in the denominator of each mini-fraction. You will then have a case (0 - 0) / (0 - 0) which will is indeterminate.

Instead, try dividing the numerator and denominator of the main fraction by x each, to get [(x + 7)/x] divided by [(3x + 5)/x].

This leads to [1 + 7/x] divided by [3 + 5/x] where the terms 7/x and 5/x will tend to zero (tiny negative value) so that the result is 1/3.

Unless you somehow proceed with dividing by x^2 and perform operations like L Hopital rule…

ahhhh i see, thank you very much! appreciate it a lot