2/m-1/m+1=5/2m+2

Solution for 2/m-1/m+1=5/2m+2 equation:

2/m-1/m+1=5/2m+2

We move all terms to the left:

2/m-1/m+1-(5/2m+2)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 2m+2)!=0

m∈R


We get rid of parentheses

2/m-1/m-5/2m-2+1=0

We calculate fractions


(-2m+2)/2m^2+(-5m)/2m^2-2+1=0

We add all the numbers together, and all the variables

(-2m+2)/2m^2+(-5m)/2m^2-1=0

We multiply all the terms by the denominator


(-2m+2)+(-5m)-1*2m^2=0

Wy multiply elements

-2m^2+(-2m+2)+(-5m)=0

We get rid of parentheses

-2m^2-2m-5m+2=0

We add all the numbers together, and all the variables

-2m^2-7m+2=0

a = -2; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·(-2)·2
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{65}}{2*-2}=\frac{7-\sqrt{65}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{65}}{2*-2}=\frac{7+\sqrt{65}}{-4}
$