((y-2)/(y+3)) - ((y)/(2y+6))?

Question

Subtract and then simplify...I tried to do it but the answers I came up with don't match the multiple choice! Please show work so I can understand what you did.

Answer 1

(y - 2)/(y + 3) - (y)/2(y+3)
2(y-2)/2(y+3) - y/2(y+3)
(2y - 4 - y)/2(y+3)
(y - 4)/2(y + 3)

Answer 2

Subtract THEN simplify? Or do you mean simplify then subtract? I am also assuming the terms equal 0. The way I would solve this is like this:

((y-2)/(y+3)) = ((y)/(2y+6))

multiply both sides by the denominator to get:
(y-2)(2y+6)=y(y+3)

expanding and simplifying:
2y^2+6y-4y-12=y^2+3y
2y^2+2y-12=y^2+3y

bringing all terms to the left hand side we get:
y^2-y-12=0

which can also be written as:
(y-4)(y+3)=0

Hope this helps!

Answer 3

to add or subtract fractions, you need common denominators.

your denominators are y+3 &2y+6

you could multiply each side by the others denominator over its self. However you can simply look at these and see that one is simply twice as much as the other, so multiply the first fractions by 2/2
this would give you
(2y-4/(2y+6)) -(y/(2y+6))
now you can combine the fractions giving you
2y-4-y
______
2y+6
combine like terms and you get
y-4
_____
2y+6

you could try to cancel something out to make it simplier, so trying to factor the bottom with y-4 times something to equal something, but you can't factor that so
(y-4)/(2y+6)
would be your answer.

that would be the same thing as
(y-4)/(2(y+3))

Answer 4

y-2 /y+3 - y/ 2(y+3)

2(y-2)-y
2y-4-y

y-4/2(y+3)

Answer 5

y-2 y
------- - -------
y+3 2x+6


y-2 y
-------- - -------
y+3 2(x+3)


2(y-2) y
--------- - ------
2(y+3) 2(y+3)


2y-4-y
---------
2(y+3)


y-4
--------
2(y+3)

Answer 6

simplifies to