2x+3/x+1=5x-6/x+1

Solution for 2x+3/x+1=5x-6/x+1 equation:

2x+3/x+1=5x-6/x+1

We move all terms to the left:

2x+3/x+1-(5x-6/x+1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

2x+3/x-5x+6/x-1+1=0

We multiply all the terms by the denominator


2x*x-5x*x-1*x+1*x+3+6=0

We add all the numbers together, and all the variables

2x*x-5x*x+9=0

Wy multiply elements

2x^2-5x^2+9=0

We add all the numbers together, and all the variables

-3x^2+9=0

a = -3; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-3)·9
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*-3}=\frac{0-6\sqrt{3}}{-6}
=-\frac{6\sqrt{3}}{-6}
=-\frac{\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*-3}=\frac{0+6\sqrt{3}}{-6}
=\frac{6\sqrt{3}}{-6}
=\frac{\sqrt{3}}{-1}
$