x+3/x+1=15/x+7=

Solution for x+3/x+1=15/x+7= equation:

x+3/x+1=15/x+7=

We move all terms to the left:

x+3/x+1-(15/x+7)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

x+3/x-15/x-7+1=0

We multiply all the terms by the denominator


x*x-7*x+1*x+3-15=0

We add all the numbers together, and all the variables

-6x+x*x-12=0

Wy multiply elements

x^2-6x-12=0

a = 1; b = -6; c = -12;
Δ = b2-4ac
Δ = -62-4·1·(-12)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*1}=\frac{6-2\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*1}=\frac{6+2\sqrt{21}}{2}
$