3/x+x=7/x

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

3/x+x=7/x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x+3/x-7/x=0

We multiply all the terms by the denominator


x*x+3-7=0

We add all the numbers together, and all the variables

x*x-4=0

Wy multiply elements

x^2-4=0

a = 1; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·1·(-4)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*1}=\frac{4}{2}
=2
$