x2-9...

obroten007 @obroten007

July 2022 1 2 Report

x/x-3 - 5/x+3 = 18/x2-9

Answers & Comments

DariosI

Verified answer

ОДЗ
х-3=0
х=3
х+3=0
х=-3
x²-9=0
(x-3)(x+3)=0
x=3
x=-3

$\frac{x}{x-3}- \frac{5}{x+3}= \frac{18}{(x+3)(x-3)}$
$\frac{x(x+3)-5(x-3)}{(x-3)(x+3)}= \frac{18}{(x+3)(x-3)}$
$\frac{ x^{2} +3x-5x+15}{(x-3)(x+3)}= \frac{18}{(x+3)(x-3)}$
$\frac{ x^{2} -2x+15}{(x-3)(x+3)}= \frac{18}{(x+3)(x-3)}$
x²-2x+15=18
x²-2x-3=0
D=4+4*3=16
x₁=(2-4)/2=-1
x₂=(2+4)/2=3

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