1/x+3/2x=1/x+1

Solution for 1/x+3/2x=1/x+1 equation:

1/x+3/2x=1/x+1

We move all terms to the left:

1/x+3/2x-(1/x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/x+3/2x-1/x-1=0

We calculate fractions


(-2x+1)/2x^2+3x/2x^2-1=0

We multiply all the terms by the denominator


(-2x+1)+3x-1*2x^2=0

We add all the numbers together, and all the variables

3x+(-2x+1)-1*2x^2=0

Wy multiply elements

-2x^2+3x+(-2x+1)=0

We get rid of parentheses

-2x^2+3x-2x+1=0

We add all the numbers together, and all the variables

-2x^2+x+1=0

a = -2; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-2)·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-2}=\frac{2}{-4}
=-1/2
$