Evaluate xx−1x+1x
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Step-by-Step Solution
Step 1: Recall Determinant Formula
To evaluate a 2×2 determinant, we multiply the elements on the main diagonal (top-left to bottom-right) and subtract the product of the elements on the anti-diagonal (top-right to bottom-left).
Step 2: Identify Elements
In the given determinant, we identify the values for a, b, c, and d by comparing it with the general form of a 2×2 determinant.
Step 3: Substitute and Simplify
Now, substitute these values into the determinant formula. We multiply x by x, and subtract the product of (x+1) and (x−1).
Step 4: Expand and Combine Terms
Expand the products. The term (x+1)(x-1) is a difference of squares, which simplifies to x2−12=x2−1. Then, distribute the negative sign and combine like terms.