(x+2)(x+3)/(x+1)(X+1)=2

Solution for (x+2)(x+3)/(x+1)(X+1)=2 equation:

(x+2)(x+3)/(x+1)(x+1)=2

We move all terms to the left:

(x+2)(x+3)/(x+1)(x+1)-(2)=0


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

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

x+1)(x!=-1

x∈R


We multiply parentheses ..

(+x^2+3x+2x+6)/(x+1)(x+1)-2=0

We multiply all the terms by the denominator


(+x^2+3x+2x+6)-2*(x+1)(x+1)=0

We get rid of parentheses

x^2+3x+2x-2*(x+1)(x+1)+6=0

We multiply parentheses ..

x^2-2*(+x^2+x+x+1)+3x+2x+6=0

We add all the numbers together, and all the variables

x^2-2*(+x^2+x+x+1)+5x+6=0

We multiply parentheses

x^2-2x^2-2x-2x+5x-2+6=0

We add all the numbers together, and all the variables

-1x^2+x+4=0

a = -1; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-1)·4
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{17}}{2*-1}=\frac{-1-\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*-1}=\frac{-1+\sqrt{17}}{-2}
$