Question

M=(N-2)/N solve for N

Answer 1

`\sf N=(-2)/((M-1))`

Explanation:

`\sf M=((N-2))/(N)`

Multiply both sides by N.

MN = N - 2

Subtract N from both sides.

MN - N = - 2

Take the Common factor "N" out.

N ( M - 1 ) = - 2

Divide both sides by ( M - 1 ).

`\sf N=(-2)/((M-1))`

Answer 2

M = (N-2)/N

M = N² - 2N

N² - 2N - M = 0

To find N we need to use quadratic formula.

For our equation x = N, a=1, b= -2, c= -M

`x=\frac{-b+/-\sqrt{b^(2)-4ac} }{2a} \\ \\N=\frac{-(-2)+/-\sqrt{(-2)^(2) -4*1*(-M)} }{2*1} \\ \\ N=(2+/-√(4+4M) )/(2) \\ \\ N=(-2+/-2√(1+M) )/(2) = -1+/-√(1+M) \\ \\ N = -1 +√(1+M) \ or\ N=-1-√(1+M)`