How do I simplify this equation further?

[musicgold]

Hi,

Please see the attached document. I don’t know how simplify the equation further. I am trying to find the relationship between i and r. D and T are constants.

Thanks.

 

[Bill Simpson]

(3+3r+r^2)/(3+3i+i^2)=d

if I haven't made any mistakes, if i!=0, if 1+r!=0

 

[musicgold]

Thanks Bill.
Your reply is not clear to me. Would you be able to show your steps?

Also, is that factorial in i!=0, if 1+r!=0 ?

 

[Mark44]

Thanks Bill.
Your reply is not clear to me. Would you be able to show your steps?

Also, is that factorial in i!=0, if 1+r!=0 ?

No, it's not factorial. The C language notation != is sometimes used for ≠, and I believe that's what Bill meant.

 

[Bill Simpson]

Multiply both sides by (1+r)^3 to get rid of the denominators. Move everything to one side of the =. Expand all the resulting powers. Discard all the v-v terms for every expression v. Your t disappears in the process. Push d to the other side of the =. Do a divide to isolate d. Divide numerator and denominator by the common terms.

And yes != was "not equal", all the divisions and multiplications in this process depend on your not multiplying or dividing by zero or the result will be meaningless.

All this is just basic algebraic manipulation and I don't even see any tricky bits.

 

[musicgold]

Thanks Bill. That is helpful.

 

[Relay]

Make your life easier by replacing (1+r) with x. Have a common denominator of x^3 and cancel it out by cross multiplying or just multiplying both sides by x^3. Remove all like terms from both sides. Then replace x with 1+r. Expand the terms and remove all like terms on both sides. At this point you should see that T cancels out completely or I made a mistake. Good Luck.