Check Whether The Following Are Quadratic Equations (X−2)(X+1)=(X−1)(X+3)

Given equation: (x − 2)(x + 1) = (x − 1)(x + 3)

=\( x (x + 1) -2 (x + 1) = x (x + 3) – 1 (x + 3) \)

= \( x^{2} + x – 2x – 2 = x^{2} + 3x – x – 3 \)

=\( x^{2} + x – 2x – 2 – x^{2} + 3x – x – 3 = 0 \)

=\( (x^{2} – x^{2}) + (x – 2x – 3x + x) – 2 + 3 = 0 \)

= 0 – 3x + 1 = 0

= -3x + 1 = 0

The obtained equation -3x + 1 = 0 is not in the form of ax^{2} + bx + c = 0

Therefore, the given equation (x − 2)(x + 1) = (x − 1)(x + 3) is not a quadratic equation

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