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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-x*x+5=0

Wy multiply elements

-1x^2+5=0

a = -1; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-1)·5
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*-1}=\frac{0-2\sqrt{5}}{-2}
=-\frac{2\sqrt{5}}{-2}
=-\frac{\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*-1}=\frac{0+2\sqrt{5}}{-2}
=\frac{2\sqrt{5}}{-2}
=\frac{\sqrt{5}}{-1}
$