(x%2B1)%3D(x-1)(x%2B3)-solution.jpeg "(x-2)(x+1)=(x-1)(x+3) Solution")
Solving the Equation: (x-2)(x+1) = (x-1)(x+3)
This equation is a quadratic equation that can be solved by expanding the products and simplifying. Here's how to do it:
1. Expand the Products:
- (x - 2)(x + 1) = x² - x - 2
- (x - 1)(x + 3) = x² + 2x - 3
2. Set the Equations Equal:
Now we have: x² - x - 2 = x² + 2x - 3
3. Simplify:
- Subtract x² from both sides: -x - 2 = 2x - 3
- Add x to both sides: -2 = 3x - 3
- Add 3 to both sides: 1 = 3x
- Divide both sides by 3: x = 1/3
Therefore, the solution to the equation (x - 2)(x + 1) = (x - 1)(x + 3) is x = 1/3.
Explanation:
This equation represents a situation where two expressions are equal. By expanding the products and simplifying, we were able to isolate the variable 'x' and find its value. This value, x = 1/3, is the solution to the equation because it makes the equation true when substituted.