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

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

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

We move all terms to the left:

(x+2)(x+3)/(x+1)(x+1)-(2/3)=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 add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

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

We calculate fractions


(-2x^2-4x-2)/(3x^2+6x+3)+(3x^2+15x+18)/(3x^2+6x+3)=0

We multiply all the terms by the denominator


(-2x^2-4x-2)+(3x^2+15x+18)=0

We get rid of parentheses

-2x^2+3x^2-4x+15x-2+18=0

We add all the numbers together, and all the variables

x^2+11x+16=0

a = 1; b = 11; c = +16;
Δ = b2-4ac
Δ = 112-4·1·16
Δ = 57
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{-(11)-\sqrt{57}}{2*1}=\frac{-11-\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{57}}{2*1}=\frac{-11+\sqrt{57}}{2}
$