Help Stuck on Algebra?

Question

I broke the rational expression down but now what do I do?
4y/(y+5) + 2y/(y-1)

Answer 1

A simplified version of this expression would be something like:

1/2 + 1/3 = ?

To find the answer to this question you have to find the lowest common multiple. Here the answer is 6 (2*3), then do this:

[(1/2) * [(3/3)] = 3/6
+
[(1/3) * 2/2] = 2/6

= 5/6

The expression that you have is just a slightly more complex version of this...

The lowest common multiple is (y+5)(y-1)...

4y/(y+5) * (y-1)/(y-1)
= 4y^2 -4y /(y+5)(y-1)

+

2y/(y-1) * (y+5)/(y+5)
=2y^2+10y/(y+5)(y-1)

=6y^2+6y / (y+5)(y-1)

Answer 2

First you have to combine the 2 terms
to do that you need get a common denominator

the numerator will look like this during the process
4y*(y-1) + 2y*(y+5) =
4y^2 - 4y + 2y^2 + 10y =
6y^2 +6y

The denominator is
(y-1)*(y+5)=
y^2 + 4y -5

so the answer is
(6y^2 +6y)/(y^2 +4y -5)

Answer 3

Give them common denominators:

4y(y-1) + 2y(y+5)
--------- ----------
(y-1)(y+5) (y-1)(y+5)

Now that they have the same denominators, you can add the numerators:

Factor to your liking

Answer 4

4y (y-1) + 2y (y+5)
------------------------- =
(y+5) (y-1)

2y^2 + 1
-----------
(y+5)(y+1)

you should be able to go from there. Good luck!

Answer 5

=4y(y-1)+2y(y+5) =4y^2-4y+2y^2+10y =6y^2+6y =6y(y+1) I think thats it...

Answer 6

common denominator...of y+5 and y-1so 4y(y-1) + 2y(y-5).....
4y^2-4y+ 2y^2-10y then combine like terms... 6y^2-14y

Answer 7

4y^2 + 20y + 2y^2 - 2y

Now simplify.

6y^2 + 18y

Answer 8

4y 2y
---- + ----
y+5 y-1

=
4y + 2y
----------
y+5+y-1

=
6y
-----
2y + 4

Answer 9

If it is equal to 0 and / means divide, then you mulitiply the entire equation by (y+5)(y-1).

Answer 10

Distribute to the numbers in the parenthesis and simplify.