(x^2-5x-6)/(x^2-1)=0

Solution for (x^2-5x-6)/(x^2-1)=0 equation:

(x^2-5x-6)/(x^2-1)=0


Domain of the equation: (x^2-1)!=0

We move all terms containing x to the left, all other terms to the right

x^2!=1

x^2!=1/

x^2!=√1/

x!=1

x∈R


We multiply all the terms by the denominator


(x^2-5x-6)=0

We get rid of parentheses

x^2-5x-6=0

a = 1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*1}=\frac{12}{2}
=6
$