Teh graph of xy-4x-2y-4=0 can be expressed as a set of parametric equations. If y = 4t/(t-3) and x= f(t), then f(t)=? The answer is t-1. Thanks for advice for tackling these in general.
First, separate the function, with terms including $\displaystyle f(t)$ on the left side of the equation and terms without an $\displaystyle f(t)$ component on the right. Then, take out a common factor of $\displaystyle f(t)$ from the left. Write everything remaining on the left as one fraction, and everything on the right as one fraction. Then divide/multiply through as necessary so that you're left with something of the form $\displaystyle f(t)=\cdots$ to simplify. If you need further help, please try this method yourself and show me how far you can get.
I still feel like you're not putting a full commitment into it.
We had:
$\displaystyle [f(t)]\frac{4t}{t-3}-4[f(t)]-2\cdot\frac{4t}{t-3}-4=0$
I then advised that you split the terms so that terms involving an $\displaystyle f(t)$ were on the left and terms without were on the right, and take a common factor of $\displaystyle f(t)$
$\displaystyle [f(t)](\frac{4t}{t-3}-4)=4+\frac{8t}{t-3}$
My next piece of advice was to rewrite everything on each side over a common denominator.
$\displaystyle [f(t)]\cdot\frac{4t-4(t-3)}{t-3}=\frac{4(t-3)+8t}{t-3}$
Now we can just multiply through by $\displaystyle (t-3)$, as my previous response implied, to get:
$\displaystyle [f(t)]\cdot [4t-4(t-3)]=[4(t-3)+8t]$
I've done the majority for you now - see if you can finish.