2x/x^2-1=5/8

Solution for 2x/x^2-1=5/8 equation:

2x/x^2-1=5/8

We move all terms to the left:

2x/x^2-1-(5/8)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

2x/x^2-1-(+5/8)=0

We get rid of parentheses

2x/x^2-1-5/8=0

We calculate fractions


(-5x^2)/8x^2+16x/8x^2-1=0

We multiply all the terms by the denominator


(-5x^2)+16x-1*8x^2=0

Wy multiply elements

(-5x^2)-8x^2+16x=0

We get rid of parentheses

-5x^2-8x^2+16x=0

We add all the numbers together, and all the variables

-13x^2+16x=0

a = -13; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-13)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-13}=\frac{-32}{-26}
=1+3/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-13}=\frac{0}{-26}
=0
$