m-1/m=1

Solution for m-1/m=1 equation:

m-1/m=1

We move all terms to the left:

m-1/m-(1)=0


Domain of the equation: m!=0

m∈R


We multiply all the terms by the denominator


m*m-1*m-1=0

We add all the numbers together, and all the variables

-1m+m*m-1=0

Wy multiply elements

m^2-1m-1=0

a = 1; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·1·(-1)
Δ = 5
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{-(-1)-\sqrt{5}}{2*1}=\frac{1-\sqrt{5}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5}}{2*1}=\frac{1+\sqrt{5}}{2}
$