Solving the Equation: (x-2)(x+1) = (x-1)(x+3)
This equation involves expanding brackets, simplifying, and then solving for x. Here's a step-by-step solution:
1. Expand the Brackets
- Left side: (x-2)(x+1) = x² - x - 2
- Right side: (x-1)(x+3) = x² + 2x - 3
2. Simplify the Equation
Now the equation looks like this: x² - x - 2 = x² + 2x - 3
3. Isolate the x Terms
Subtract x² from both sides: -x - 2 = 2x - 3
4. Combine Like Terms
Add x to both sides: -2 = 3x - 3
Add 3 to both sides: 1 = 3x
5. Solve for x
Divide both sides by 3: x = 1/3
Solution
Therefore, the solution to the equation (x-2)(x+1) = (x-1)(x+3) is x = 1/3.