(x-2)(x+1)=(x-1)(x+3) Solution

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Jun 07, 2024

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Solving the Equation: (x-2)(x+1) = (x-1)(x+3)

In this article, we will solve the equation (x-2)(x+1) = (x-1)(x+3) using the properties of algebra.

Expanding the Equation

To start, let's expand both sides of the equation using the distributive property:

Left Side:

(x-2)(x+1) = x^2 - x - 2

Right Side:

(x-1)(x+3) = x^2 + 2x - 3

Now, we can equate both sides of the equation:

x^2 - x - 2 = x^2 + 2x - 3

Simplifying the Equation

Let's simplify the equation by combining like terms:

-x - 2 = 2x - 3

Adding 2x to Both Sides

Add 2x to both sides of the equation to get:

-3x - 2 = -3

Adding 2 to Both Sides

Add 2 to both sides of the equation to get:

-3x = -1

Dividing Both Sides by -3

Divide both sides of the equation by -3 to get:

x = 1/3

Conclusion

Therefore, the solution to the equation (x-2)(x+1) = (x-1)(x+3) is x = 1/3.