# Thread: Anyone help w/ "3tx=4(t-1)(x+1) is x(t)= 4(t-1) / (4-t)"

1. ## Anyone help w/ "3tx=4(t-1)(x+1) is x(t)= 4(t-1) / (4-t)"

Can't work out how the answer to this:

3tx=4(t-1)(x+1)

is

x(t)= 4(t-1) / (4-t)

2. Originally Posted by Flatty
Can't work out how the answer to this:

3tx=4(t-1)(x+1)

is

x(t)= 4(t-1) / (4-t)
What did you try? Where did you get stuck?

I started by expanding the right-hand side, followed by separating x-terms to one side of the equation and remaining terms to the other side.

3. Originally Posted by Flatty
Can't work out how the answer to this:

3tx=4(t-1)(x+1)

is

x(t)= 4(t-1) / (4-t)
What you've posted is a sentence without context. There is no question to "answer".

Was the complete original equation something along the lines of the following?

Given the equation $3tx\, =\, 4\, (t\, -\, 1)\, (x\, +\, 1),$ rearrange to express $x$ as a $\mbox{func}\mbox{tion}$ of $t.$

If so, are you stuck in the algebra? Are you not familiar with "functions"? If not, what is the actual "question"?

4. The original question is solve the following initial value problems

t(t-1) dx/dt = x(x+1); where x(2)=2

I'm just stuck with the last stage of the algebra, i can re arrange into its separable form, take the partial fraction, integrate etc just the last part of the algebra is where I'm stuck.

ie. not sure how to multiply both sides by (x+1) to solve for x

5. Originally Posted by Flatty
… not sure how to multiply both sides by (x+1) to solve for x
That single step will not solve for x. It will complicate the process, by creating a quadratic factor in x (on the right-hand side).

Did you try my suggestion? It's a fairly straightforward approach, and I'm confident that you can do it.

6. nope don't know where to even start

7. Could you point me in the right direction with a youtube vid?

i know its straight forward just missing something obvious

8. Originally Posted by Flatty
nope don't know where to even start
Is this because you do not understand the wording in my suggestion or is it because you don't know how to multiply one binomial expression by another?

(Your math course was supposed to teach you how to multiply binomial expressions, before giving you this exercise.)

The right-hand side of the given equation is:

4(t-1)(x+1)

This expression is the constant 4 times the binomial (t-1) times the binomial (x+1).

Have you heard of the FOIL method for multiplying expressions like (t-1)(x+1)? If not, maybe you heard it described as double-distribution.

Using FOIL (aka double-distribution) to multiply (t-1)(x+1) is my suggestion, for the first step.

Next, multiply your result by 4.

Show us your work, up to this point, and we can go from there.

9. Originally Posted by Flatty
Could you point me in the right direction with a youtube vid?
I still don't know for sure why you're stuck because your answer to my question is too vague.

Here's a video about how to multiply two binomial expressions:

If your issue has to do with something else, please be specific and explain what it is.

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