Let's take an equation

x^{2} - y^{2} = x^{2} - y^{2}

Here, L.H.S = R.H.S.

Now, let's take L.H.S. first.

L.H.S. = x^{2} - y^{2}

Here we can apply formula of (a^{2} - b^{2}) = (a + b)(a - b)

∴ x^{2} - y^{2} = (x + y)(x - y)

Now let's assume x = y ...... (1)

∴ L.H.S. = (x + x)(x - x) ...... (2)

Now let's take R.H.S.

R.H.S. = x^{2} - y^{2}

Since x = y (from equation 1)

∴ R.H.S. = x^{2} - x^{2}

Since we can take x as common

∴ R.H.S. = x(x -x) ...... (3)

Since, L.H.S = R.H.S.

∴ (x + x)(x - x) = x(x -x) ...... (from euqation 2 and 3)

We can cancel (x - x) from both the sides.

∴ (x + x) = x

∴ 2x = x

We can cancel x from both the sides so,

∴ 2 = 1 OR 1 = 2

∴ 1 = 2 ...... (4)