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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


x*x+1*x+1*x-2-5-7=0

We add all the numbers together, and all the variables

2x+x*x-14=0

Wy multiply elements

x^2+2x-14=0

a = 1; b = 2; c = -14;
Δ = b2-4ac
Δ = 22-4·1·(-14)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{15}}{2*1}=\frac{-2-2\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{15}}{2*1}=\frac{-2+2\sqrt{15}}{2}
$