(x-4/x-3)=1

Solution for (x-4/x-3)=1 equation:

(x-4/x-3)=1

We move all terms to the left:

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


Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

x-4/x-3-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-4x+x*x-4=0

Wy multiply elements

x^2-4x-4=0

a = 1; b = -4; c = -4;
Δ = b2-4ac
Δ = -42-4·1·(-4)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2}}{2*1}=\frac{4-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*1}=\frac{4+4\sqrt{2}}{2}
$