3/x+2/(x+1)=5

Solution for 3/x+2/(x+1)=5 equation:

3/x+2/(x+1)=5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

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

x!=-1

x∈R


We calculate fractions


(3x+3)/(x^2+x)+2x/(x^2+x)-5=0

We multiply all the terms by the denominator


(3x+3)+2x-5*(x^2+x)=0

We add all the numbers together, and all the variables

2x+(3x+3)-5*(x^2+x)=0

We multiply parentheses

-5x^2+2x+(3x+3)-5x=0

We get rid of parentheses

-5x^2+2x+3x-5x+3=0

We add all the numbers together, and all the variables

-5x^2+3=0

a = -5; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-5)·3
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-5}=\frac{0-2\sqrt{15}}{-10}
=-\frac{2\sqrt{15}}{-10}
=-\frac{\sqrt{15}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-5}=\frac{0+2\sqrt{15}}{-10}
=\frac{2\sqrt{15}}{-10}
=\frac{\sqrt{15}}{-5}
$