m/2m+1+1=2/m-3

Solution for m/2m+1+1=2/m-3 equation:

m/2m+1+1=2/m-3

We move all terms to the left:

m/2m+1+1-(2/m-3)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: m-3)!=0

m∈R


We add all the numbers together, and all the variables

m/2m-(2/m-3)+2=0

We get rid of parentheses

m/2m-2/m+3+2=0

We calculate fractions


m^2/2m^2+(-4m)/2m^2+3+2=0

We add all the numbers together, and all the variables

m^2/2m^2+(-4m)/2m^2+5=0

We multiply all the terms by the denominator


m^2+(-4m)+5*2m^2=0

Wy multiply elements

m^2+10m^2+(-4m)=0

We get rid of parentheses

m^2+10m^2-4m=0

We add all the numbers together, and all the variables

11m^2-4m=0

a = 11; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·11·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*11}=\frac{0}{22}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*11}=\frac{8}{22}
=4/11
$