(x-7)(x+1)/(x+1)(x-5)=0

Solution for (x-7)(x+1)/(x+1)(x-5)=0 equation:

(x-7)(x+1)/(x+1)(x-5)=0


Domain of the equation: (x+1)(x-5)!=0

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

x+1)(x!=5

x∈R


We multiply parentheses ..

(+x^2+x-7x-7)/(x+1)(x-5)=0

We multiply all the terms by the denominator


(+x^2+x-7x-7)=0

We get rid of parentheses

x^2+x-7x-7=0

We add all the numbers together, and all the variables

x^2-6x-7=0

a = 1; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·1·(-7)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8}{2*1}=\frac{14}{2}
=7
$