5x-4/x+2=3x+1/x-1

Solution for 5x-4/x+2=3x+1/x-1 equation:

5x-4/x+2=3x+1/x-1

We move all terms to the left:

5x-4/x+2-(3x+1/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

5x-4/x-3x-1/x+1+2=0

We multiply all the terms by the denominator


5x*x-3x*x+1*x+2*x-4-1=0

We add all the numbers together, and all the variables

3x+5x*x-3x*x-5=0

Wy multiply elements

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

We add all the numbers together, and all the variables

2x^2+3x-5=0

a = 2; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·2·(-5)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-7}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*2}=\frac{4}{4}
=1
$