1/x+1/x-10=X-9/x-10

Solution for 1/x+1/x-10=X-9/x-10 equation:

1/x+1/x-10=x-9/x-10

We move all terms to the left:

1/x+1/x-10-(x-9/x-10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-10)!=0

x∈R


We get rid of parentheses

1/x+1/x-x+9/x+10-10=0

We multiply all the terms by the denominator


-x*x+10*x-10*x+1+1+9=0

We add all the numbers together, and all the variables

-x*x+11=0

Wy multiply elements

-1x^2+11=0

a = -1; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-1)·11
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{11}}{2*-1}=\frac{0-2\sqrt{11}}{-2}
=-\frac{2\sqrt{11}}{-2}
=-\frac{\sqrt{11}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{11}}{2*-1}=\frac{0+2\sqrt{11}}{-2}
=\frac{2\sqrt{11}}{-2}
=\frac{\sqrt{11}}{-1}
$