3(1+x)/4x=1-1/x

Solution for 3(1+x)/4x=1-1/x equation:

3(1+x)/4x=1-1/x

We move all terms to the left:

3(1+x)/4x-(1-1/x)=0


Domain of the equation: 4x!=0

x!=0/4

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+1)/4x-(-1/x+1)=0

We get rid of parentheses

3(x+1)/4x+1/x-1=0

We calculate fractions


(3x^2+3x)/4x^2+4x/4x^2-1=0

We multiply all the terms by the denominator


(3x^2+3x)+4x-1*4x^2=0

We add all the numbers together, and all the variables

4x+(3x^2+3x)-1*4x^2=0

Wy multiply elements

-4x^2+4x+(3x^2+3x)=0

We get rid of parentheses

-4x^2+3x^2+4x+3x=0

We add all the numbers together, and all the variables

-1x^2+7x=0

a = -1; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-1)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-1}=\frac{0}{-2}
=0
$