3/x+x-9-7/x-3=-4/x+3

Solution for 3/x+x-9-7/x-3=-4/x+3 equation:

3/x+x-9-7/x-3=-4/x+3

We move all terms to the left:

3/x+x-9-7/x-3-(-4/x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We add all the numbers together, and all the variables

x+3/x-7/x-(-4/x+3)-12=0

We get rid of parentheses

x+3/x-7/x+4/x-3-12=0

We multiply all the terms by the denominator


x*x-3*x-12*x+3-7+4=0

We add all the numbers together, and all the variables

-15x+x*x=0

Wy multiply elements

x^2-15x=0

a = 1; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·1·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*1}=\frac{30}{2}
=15
$