SOLVE Y/(Y+4)-2/Y= (Y+2)/4

[Stine]

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

SO FAR THIS IS WHAT I HAVE:

Y(Y+4)* Y/(Y+4) -2/Y*Y(Y+4)= (Y+2)/4*Y(Y+4)

LEFT SIDE:
=-2Y-8
RIGHT SIDE:
I AM NOT SURE WHAT I AM SUPPOSED TO CANCEL ON THIS SIDE.

AM I ON THE RIGHT TRACK AND CAN SOMEONE HELP ME WITH THE RIGHT SIDE OF THIS PROBLEM????

THANK YOU!

 

[tkhunny]

I AM NOT SURE WHAT I AM SUPPOSED TO CANCEL ON THIS SIDE.

I REALLY do not like this language. It does not encourage me to believe you are thinking correctly.

Y/(Y+4)-2/Y= (Y+2)/4

Domain issues: Y CANNOT be 0 or -4. Do you see why?

Y/(Y+4)-2/Y= (Y+2)/4

Solving: One piece at a time. No need to blast it with a cannon when a flyswatter will do.

Multiply by (Y+4) -- Why did I pick that?

Y-2(Y+4)/Y= (Y+2)(Y+4)/4

Multiply by Y

Y^2 - 2(Y+4)= (Y+2)(Y+4)*Y/4

Multiply by 4

4Y^2 - 8(Y+4)= (Y+2)(Y+4)*Y

Expand

4Y^2 - 8Y - 32 = (Y^2 +6Y +8)*Y = Y^3 + 6Y^2 + 8Y

Subtract 4Y^2

- 8Y - 32 = Y^3 + 2Y^2 + 8Y

Add 8Y

- 32 = Y^3 + 2Y^2 + 16Y

Add 32

0 = Y^3 + 2Y^2 + 16Y + 32

There are NO positive solutions. Do you know how to tell, just from looking?

Y = -2 looks suspicious. Try it out - synthetic division? And we see:

Y^3 + 2Y^2 + 16Y + 32 = (Y+2)(Y^2 + 16) = 0

Looks like we're done.

 

[stapel]

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

SO FAR THIS IS WHAT I HAVE....

In the future, please post replies to the original thread, rather than starting a whole new thread on the same exercise.

Thank you.

Eliz.

 

[Stine]

Thank you for your help

I really would like to thank you for your help. Since I am not sure on the math language I am going to continue to do my best at posting of my questions.