Simplify the rational function (frac{x^3 - x^2 - x + 1}{x^2 - 1})

Question

Accepted Answer

Step:1 ：Factor the numerator and the denominator. The numerator (x^3 - x^2 - x + 1) can be factored into ((x - 1)(x^2 + 1)), and the denominator (x^2 - 1) can be factored into ((x - 1)(x + 1))Step:2 ：Now we have (frac{(x - 1)(x^2 + 1)}{(x - 1)(x + 1)})Step:3 ：Cancel the common factor ((x - 1)) from the numerator and the denominatorStep:4 ：Hence the simplified form of the given rational function is (frac{x^2 + 1}{x + 1})

Answer

Step: 1 ：Factor the numerator and the denominator. The numerator (x^3 - x^2 - x + 1) can be factored into ((x - 1)(x^2 + 1)), and the denominator (x^2 - 1) can be factored into ((x - 1)(x + 1))Step: 2 ：Now we have (frac{(x - 1)(x^2 + 1)}{(x - 1)(x + 1)})Step: 3 ：Cancel the common factor ((x - 1)) from the numerator and the denominatorStep: 4 ：Hence the simplified form of the given rational function is (frac{x^2 + 1}{x + 1})

Simplify the rational function $\frac{x^{3} - x^{2} - x + 1}{x^{2} - 1}$

Answer

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Simplify the rational function $\frac{x^{3} - x^{2} - x + 1}{x^{2} - 1}$