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:
- -x - 2 = 2x - 3
3. Isolating x
To isolate x, we can add x to both sides and add 3 to both sides:
- 1 = 3x
4. Solving for x
Finally, we divide both sides by 3 to find the solution for x:
- x = 1/3
Therefore, the solution to the equation (x-2)(x+1) = (x-1)(x+3) is x = 1/3.