How to represent a fractional function in a simplified form?

The answer is as follows:

Presuming that is:

y = (2x - 3) / (x + 1)

Divide to get a quotient (alpha) and a remainder (beta):

. . . . .__2__
x + 1 ) 2x - 3
. . . . . .2x + 2
. . . . . ---------
. . . . . . . . . -5

So this turns into:

y = 2 - 5 / (x + 1)

y = 2x-3/x+1 ??
using the rules of precedence, that is
y = 2x - (3/x) + 1
is that correct?

Mistake: it should be(2x-3)/(x+1).
(2x-3)/(x+1)
=
[2(x+1)-5]/(x+1)
=
2(x+1)/(x+1)-5/(x+1)
=
2-5/(x+1)

What you mean is y = (2x - 3)/(x + 1)

i.e. 2(x + 1)/(x + 1) - 5/(x + 1)

so, y = 2 - 5/(x + 1)

Note: The answer from Uncle Michael is excellent, much clearer...so, not worthy of a thumbs down!!

:)>

The picture is correct. [Your stating of the function is wrong because you did not use delimiters to replicate what the picture says.  PEDMAS turns your function/expression into 2x - (3/x) + 1.  Multiply through by x === 2x^2 -3 + x === 2x^2 + x - 3] To express it on one line to be read/understood by a computer  y = 2x - (3/(x+1)).  In other words, I just substituted in to represent the form you typed.  Plug in a few sets of numbers for the variables to verify and see that it works/is correct.  [I am assuming the x in the picture is not the same as the x in the function.  btw, those variable are alpha, beta, and gamma.]  Note: Michael ASSUMES parentheses whereas you do not show any. EDIT - Uncle Michael only gets a thumbs down because he ASSUMED parantheses (unlike people who said "If you mean ...). Computers do not assume parentheses !!