8/2m+1-1/m-2=5/2m+1

Solution for 8/2m+1-1/m-2=5/2m+1 equation:

8/2m+1-1/m-2=5/2m+1

We move all terms to the left:

8/2m+1-1/m-2-(5/2m+1)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: m!=0

m∈R



Domain of the equation: 2m+1)!=0

m∈R


We add all the numbers together, and all the variables

8/2m-1/m-(5/2m+1)-1=0

We get rid of parentheses

8/2m-1/m-5/2m-1-1=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-5m+8)/2m^2+(-2m)/2m^2-2=0

We multiply all the terms by the denominator


(-5m+8)+(-2m)-2*2m^2=0

Wy multiply elements

-4m^2+(-5m+8)+(-2m)=0

We get rid of parentheses

-4m^2-5m-2m+8=0

We add all the numbers together, and all the variables

-4m^2-7m+8=0

a = -4; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·(-4)·8
Δ = 177
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{177}}{2*-4}=\frac{7-\sqrt{177}}{-8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{177}}{2*-4}=\frac{7+\sqrt{177}}{-8}
$