x+4/x-3+1=7/x-3

Solution for x+4/x-3+1=7/x-3 equation:

x+4/x-3+1=7/x-3

We move all terms to the left:

x+4/x-3+1-(7/x-3)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

x+4/x-(7/x-3)-2=0

We get rid of parentheses

x+4/x-7/x+3-2=0

We multiply all the terms by the denominator


x*x+3*x-2*x+4-7=0

We add all the numbers together, and all the variables

x+x*x-3=0

Wy multiply elements

x^2+x-3=0

a = 1; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·1·(-3)
Δ = 13
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{-(1)-\sqrt{13}}{2*1}=\frac{-1-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*1}=\frac{-1+\sqrt{13}}{2}
$