Question

I need help with #1. I’m very confused on it.

Answer 1

$x^2 - 6x +3=0$

$x = 5.45$ and 0.55

Step-by-step explanation:

$\frac{3}{x+4} -\frac{2}{x-1} =\frac{x^2-5x-6}{x^2+3x-4}$

⇔$\frac{3(x-1)-2(x+4)}{(x-1)(x+4)}$$=\frac{x^2-5x-6}{x^2+3x-4}$

⇔$\frac{3x -1 -2x -8}{x^2+3x-4}$ $=\frac{x^2-5x-6}{x^2+3x-4}$

⇔$x-9=\frac{(x^2-5x-6)(x^2+3x-4)}{(x^2+3x-4)}$

⇔$x-9=x^2-5x -6$

⇔$x^2-5x -6 -x +9=0$

⇔$x^2 - 6x +3=0$

⇔$x = \frac{6\pm \sqrt{6^2-4.3.1} }{2.1}$

⇔$x = \frac{6\pm \sqrt{24} }{2.1}$

⇔$x=\frac{3\pm \sqrt{6} }{1}$

⇔$x = 3 \pm \sqrt{6}$

⇔$x = 5.45$ and 0.55