Question

How to divide problems like the following: (y+2)/(y+6) ....... don't know where to start, I know the answer but I don't know how to get it myself. Even a helpful video link will suffice.

Answer 1

the numerator and denominator both have degree 1, so you will get a number, plus a remainder
there is an easy trick for this
would you like to see it?

Answer 2

yes please !

Answer 3

in other words, you know when you divide it will be \[\frac{y+2}{y+6}=1+\frac{\text{some number}}{y+6}\]

Answer 4

the only question is, what is the number up top
since you know \(y\) goes in to \(y\) one time
here is the trick

Answer 5

\[\frac{y+2}{y+6}=\frac{y+6-4}{y+6}=\frac{y+6}{y+6}-\frac{4}{y+6}=1-\frac{4}{y+6}\]

Answer 6

you can do it mentally pretty much, i just wrote out the steps to show what i was doing

Answer 7

you can also do long division but
a) it takes longer and
b) i can't write long division here

Answer 8

Oh i see, but why 4 ?

Answer 9

lets go slow

Answer 10

the denominator is \(y+6\) so i forced the numerator to be \(y+6\) as well, by adding and subtracting \(4\) up top

Answer 11

i wrote \[y+2\] as \[y+6-4\] in other wrods

Answer 12

that way i get the 1 i need \[\frac{y+6}{y+6}=1\] and the remainder is \(-4\)

Answer 13

I think i get what you mean.

Answer 14

Thank you!