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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+3/x-5/x-7=0

We multiply all the terms by the denominator


x*x-7*x+3-5=0

We add all the numbers together, and all the variables

-7x+x*x-2=0

Wy multiply elements

x^2-7x-2=0

a = 1; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·1·(-2)
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{-(-7)-\sqrt{57}}{2*1}=\frac{7-\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{57}}{2*1}=\frac{7+\sqrt{57}}{2}
$