Question 329612
I went through the calculations and I got the same answer you got.


Your final solution was:


–ax + ab – a2 = –bx + b2 – ab

Both sides of this equation have a common factor:
a(–x + b – a) = b(–x + b – a)

Divide both sides by (-x+b-a):
a(–x + b – a) = b(–x + b – a)
–x + b – a –x + b – a

a = b


You got the right solution because you did all the intermediate steps correctly.


The flaw is as follows:


Start from:


a(–x + b – a) = b(–x + b – a)


Substitute (b-a) for x since this is the premise that you started with.


You get:


a * (-(b-a) + b - a) = b * (-(b-a) + b - a)


Simplify to get:


a * (-b + a + b - a) = b * (-b + a + b - a)


simplify further to get:


a * 0 = b * 0


Which will always be true regardless of the values of a or b.


Furthermore, you cannot divide by (-b + a + b - a) because division by 0 is not allowed.