# Math Help - isolating x when f(x) is a rational function of degree2 / degree1

1. ## isolating x when f(x) is a rational function of degree2 / degree1

ex. y = (x^2 + 3) / (x - 1)

cant seem to isolate the x squared. also the eq. can be rewritten as

y = (x+1) + (4 / (x-1))

help would be appreciated

2. ## Re: isolating x when f(x) is a rational function of degree2 / degree1

also, cant use calulus, must solve algebraically

3. ## Re: isolating x when f(x) is a rational function of degree2 / degree1

Hello, mzez!

$\text{Solve for }x\!:\;y \:=\: \frac{x^2 + 3}{x - 1}$

We have: . $y(x-1) \:=\:x^2+3 \quad\Rightarrow\quad xy - y \:=\:x^2+3 \quad\Rightarrow\quad x^2 - yx + (y+3) \:=\:0$

Quadratic Formula: . $x \;=\;\frac{y \pm \sqrt{y^2 - 4(y+3)}}{2}$

. . . . . . Therefore: . $x \;=\;\frac{y \pm \sqrt{y^2 - 4y - 12}}{2}$