%2F(1-x).jpeg "(1-x^2)/(1-x)")
Simplifying the Expression (1-x^2)/(1-x)
The expression (1-x^2)/(1-x) can be simplified using algebraic manipulation. Here's how:
Factoring the Numerator
The numerator, (1-x^2), is a difference of squares, which can be factored as:
(1-x^2) = (1+x)(1-x)
Simplifying the Expression
Now we can rewrite the original expression:
(1-x^2)/(1-x) = [(1+x)(1-x)]/(1-x)
Since (1-x) appears in both the numerator and denominator, we can cancel it out:
(1-x^2)/(1-x) = (1+x)
However, it's important to note that this simplification is valid only when x ≠ 1. If x = 1, the original expression becomes undefined as it results in division by zero.
Final Result
Therefore, the simplified form of (1-x^2)/(1-x) is (1+x), with the restriction that x ≠ 1.