inverse function

[spacewater]

problem
$\displaystyle f(x) = \frac {3x}{x-5}$
steps
$\displaystyle y = \frac{3x}{x-5}$

$\displaystyle x = \frac {3y}{y-5}$

$\displaystyle x(y+5)=\frac{3y}{y-5}\cdot\frac{y+5}{y+5}$

$\displaystyle xy + 5x = \frac {3y}{y+5}$

well this is where my endeavor ends... been a confusing trip but without any solution... care for help? the final coming up next week.. :roll:

 

[Aladdin]

$\displaystyle 3x=xy-5y$

$\displaystyle 3x-xy=-5y$

$\displaystyle x(3-y)=-5y$

$\displaystyle x=\frac{-5y}{3-y}$

$\displaystyle y=\frac{-5x}{3-x}$

 

[Loren]

problem
$\displaystyle f(x) = \frac {3x}{x-5}$
steps
$\displaystyle y = \frac{3x}{x-5}$

$\displaystyle x = \frac {3y}{y-5}$

$\displaystyle x(y+5)=\frac{3y}{y-5}\cdot\frac{y+5}{y+5}$ <<<should be $\displaystyle x(y-5)=3y$
then xy-5x=3y
xy-3y=5x
y(x-3) = 5x
$\displaystyle y=\frac{5x}{x-3}$ Done?

$\displaystyle xy + 5x = \frac {3y}{y+5}$

well this is where my endeavor ends... been a confusing trip but without any solution... care for help? the final coming up next week.. :roll: