In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

Let (x – a)/(x – b) = y and a/b = c

⇒ cy² + c = c²y + y

⇒ cy² – c²y –y + c = 0

⇒ cy(y – c) – 1(y – c) = 0

⇒ (cy – 1)(y – c) = 0

⇒ y = 1/c, c

⇒ ax – a² = bx – b²

⇒ x(a – b) = a² – b²

⇒ x = a + b

Also, bx – ab = ax – ab

⇒ (b – a)x = 0

⇒ x = 0