algerba help?

Question

2x-3 over 2x is equvialent to what expression?

Answer 1

1 - 3/2 x

Answer 2

are you saying ;
read as "2x-3 All over 2x"?

This is a sucker question that beginning algebra students cancel and get an answer of-3. But 2x-3 is a package, and you cannot cancel over a + or - sign. Think of the big division bar as a grouping symbol

(2x-3)
---------- already simplified

2x

You don't get to grab that 2x out of that () group. if the top were all multiplication, but say,

2xyz
--------
2x

Then you could cancel the 3x and have an answer of yz


(everything has a denominatior of 1 unless it tells you otherwise, and we generally never write the 1 as the most simplified answer.)

You could simplify it another way, by distributing the denominator, and the answer is equivalent, but most books prefer the above. The other way is:

2x - 3
----- -----
2x 2x

Anything over itself is one, so this answer is:
( 1 ) - ( 3)
------- ----
(1) (2x)

But you have changed a monomial to a bi-nomial, and for the most part, books don't want you do do that..... Omit the ( ) The computer would't write it any other way.. Drop the first demonimator, the computer wouldn't write it any other way, so it should read:
one minus, new term 3 over 2x: (1-3over2x)

Answer 3

(2x-3)/2x

separate the two numerators
(2x/2x)-(3/2x)

2x/2x is the same as 1
=1-(3/2x)

Answer 4

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