(m+5/m)-3=6/m+3

Solution for (m+5/m)-3=6/m+3 equation:

(m+5/m)-3=6/m+3

We move all terms to the left:

(m+5/m)-3-(6/m+3)=0


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R



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

m∈R


We add all the numbers together, and all the variables

(+m+5/m)-(6/m+3)-3=0

We get rid of parentheses

m+5/m-6/m-3-3=0

We multiply all the terms by the denominator


m*m-3*m-3*m+5-6=0

We add all the numbers together, and all the variables

-6m+m*m-1=0

Wy multiply elements

m^2-6m-1=0

a = 1; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·1·(-1)
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{10}}{2*1}=\frac{6-2\sqrt{10}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{10}}{2*1}=\frac{6+2\sqrt{10}}{2}
$