5/2x+1=7/x+3

Solution for 5/2x+1=7/x+3 equation:

5/2x+1=7/x+3

We move all terms to the left:

5/2x+1-(7/x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/2x-7/x-3+1=0

We calculate fractions


5x/2x^2+(-14x)/2x^2-3+1=0

We add all the numbers together, and all the variables

5x/2x^2+(-14x)/2x^2-2=0

We multiply all the terms by the denominator


5x+(-14x)-2*2x^2=0

Wy multiply elements

-4x^2+5x+(-14x)=0

We get rid of parentheses

-4x^2+5x-14x=0

We add all the numbers together, and all the variables

-4x^2-9x=0

a = -4; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-4)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-4}=\frac{18}{-8}
=-2+1/4
$