Simple quadratic equation? (but not for me!)?

2a-1 = a+1/a-1
(2a-1)(a-1) = a+1 -->multiply both sides by a-1
2a^2-4a = 0 --> Used FOIL and then subtracted a and 1 from both sides
2a(a-2) = 0 --> Factor the problem then find when it equals 0
2a = 0
a = 0
a-2 = 0
a = 2
a = 0,2

2a - 1 = (a + 1)/(a - 1)
(2a - 1)(a - 1) = a + 1
2a² - 2a - a + 1 = a + 1
2a² = 4a
2a²/2a = 4a/2a
a = 2

Answer: a = 2

Proof:
2(2) - 1 = (2 + 1)/(2 - 1)
4 - 1 = 3/1
3 = 3

2a - 1 = (a + 1)/(a - 1)
(2a - 1)(a - 1) = a + 1
2a*a - 1*a - 2a*1 + 1*1 = a + 1
2a^2 - a - 2a + 1 = a + 1
2a^2 - 3a + 1 - a - 1 = 0
2a^2 - 4a = 0
2a(a - 2) = 0

2a = 0
a = 0/2
a = 0

a - 2 = 0
a = 2

∴ a = 0 , 2

(2a-1) ( a-1) = a+1
2a^2 -3a + 1 = a + 1
2a^2 - 4a = 0
2a(a - 2 ) = 0
Therefore, a = 0 or 2

multiply both sides by a-1

(2a-1)(a-1) = a+1
2a^2 - 3a +1 -a -1 = 0
2a^2 - 4a = 0

x = (4 + sqrt 16 - 0)/4 = 2
x = (4 - sqrt 16 - 0)/4 = 0

2a - 1 = a+1/a-1

First get rid of the bottom line by multiplying both sides by a-1

(a-1)(2a-1) = a+1

2a^2 - 3a = a+1

2a^2 - 3a -a -1 = 0

2a^2 - 4a - 1 = 0

I can't factorise it, but I'll try completing the square

First I'll half it, giving

a^2 - 2a - 1/2 = 0

Now get it in another form

a^2 - 2a = 1/2

Now half the coefficient of a and square it and add it to each side

a^2 - 2a + 1 = 3/2

Now factorise

(a - 1 )(a - 1 ) = 3/2

(a-1)^2 = 3/2

So a-1 = root 3/2

So a-1 = + or - 1.22

So a = 1.22 + 1 = 2.22

OR a = - 1.22 + 1 = 0.22

So solution is 2.22 or 0.22


If you don't like completing the square, use the quadratic formula.

Remember to use brackets.
2a - 1 = (a + 1) / (a - 1)
(2a - 1)(a - 1) = a + 1
2a² - 3a + 1 = a + 1
2a² - 4a = 0
2a (a - 2) = 0
a = 0 , a = 2

a = 2