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

2 min read Jun 17, 2024

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

This equation involves expanding brackets and then solving for x. Let's break it down step-by-step:

1. Expanding the Brackets

First, we expand both sides of the equation using the distributive property (also known as FOIL):

Left side: (x-2)(x+1) = x(x+1) - 2(x+1) = x² + x - 2x - 2 = x² - x - 2
Right side: (x-1)(x+3) = x(x+3) - 1(x+3) = x² + 3x - x - 3 = x² + 2x - 3

Now our equation becomes: x² - x - 2 = x² + 2x - 3

2. Simplifying the Equation

We can simplify the equation by subtracting x² from both sides:

3. Isolating x

To isolate x, we can add x to both sides and add 3 to both sides:

4. Solving for x

Finally, we divide both sides by 3 to find the solution for x:

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