x-2/x+1=5/x+1-7

Solution for x-2/x+1=5/x+1-7 equation:

x-2/x+1=5/x+1-7

We move all terms to the left:

x-2/x+1-(5/x+1-7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+1-7)!=0

We move all terms containing x to the left, all other terms to the right

x-7)!=-1

x∈R


We add all the numbers together, and all the variables

x-2/x-(5/x-6)+1=0

We get rid of parentheses

x-2/x-5/x+6+1=0

We multiply all the terms by the denominator


x*x+6*x+1*x-2-5=0

We add all the numbers together, and all the variables

7x+x*x-7=0

Wy multiply elements

x^2+7x-7=0

a = 1; b = 7; c = -7;
Δ = b2-4ac
Δ = 72-4·1·(-7)
Δ = 77
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{-(7)-\sqrt{77}}{2*1}=\frac{-7-\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{77}}{2*1}=\frac{-7+\sqrt{77}}{2}
$