Need Help Solving a problem that involves fractions (provided scan)

[jayson]

If anyone is able to take this problem and list the steps taken to solve the problem then I would appreciate it. I know I have to multiply the gcm of the denominators by each fraction.
I have tried to do that but I have failed to get the problem right. Please help me any way you can. If you can scan back the resolution to this problem let me know.

Please open the jpeg attachment below!

 

[jayson]

You have (I think!) J / (3+y) = 3y / (y+3) - (3y+4) / (2y+6)
Re-arrange:
(3y+4) / [2(y+3)] = (3y-J) / (y+3)
Carry on...

5/(3+y) = 3y/(y+3) - (3y+4) / (2y+6)

Almost right!

Just the J is really a 5.

 

[jayson]

What is the GCF of this problem? And how did you get it?

 

[galactus]

You have a y+3 and a 2(y+3) in the denominator. Thus, the GCF is 2(y+3)

Multiply through by the GCF and cancel accordingly.

The fractions will be eliminated and you will have a simple linear equation to solve.

Be careful of the negative on the right side. That throws many students who end up using the incorrect sign.

\(\displaystyle 2(y+3)\cdot \frac{5}{y+3}=2(y+3)\cdot \frac{3y}{y+3}-2(y+3)\cdot \frac{3y+4}{2(y+3)}\)