(5x-3)/(x-1)+3/x=0

Solution for (5x-3)/(x-1)+3/x=0 equation:

(5x-3)/(x-1)+3/x=0


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

We move all terms containing x to the left, all other terms to the right

x!=1

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


(5x^2-3x)/(x^2-1x)+(3x-3)/(x^2-1x)=0

We multiply all the terms by the denominator


(5x^2-3x)+(3x-3)=0

We get rid of parentheses

5x^2-3x+3x-3=0

We add all the numbers together, and all the variables

5x^2-3=0

a = 5; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·5·(-3)
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{-(0)-2\sqrt{15}}{2*5}=\frac{0-2\sqrt{15}}{10}
=-\frac{2\sqrt{15}}{10}
=-\frac{\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*5}=\frac{0+2\sqrt{15}}{10}
=\frac{2\sqrt{15}}{10}
=\frac{\sqrt{15}}{5}
$