2x-7/x-3=x+1

Solution for 2x-7/x-3=x+1 equation:

2x-7/x-3=x+1

We move all terms to the left:

2x-7/x-3-(x+1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2x-7/x-x-1-3=0

We multiply all the terms by the denominator


2x*x-x*x-1*x-3*x-7=0

We add all the numbers together, and all the variables

-4x+2x*x-x*x-7=0

Wy multiply elements

2x^2-1x^2-4x-7=0

We add all the numbers together, and all the variables

x^2-4x-7=0

a = 1; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·1·(-7)
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{-(-4)-2\sqrt{11}}{2*1}=\frac{4-2\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{11}}{2*1}=\frac{4+2\sqrt{11}}{2}
$