(1-(1)/(x))/(1-(1)/(x^(2)))

Understand given expression: Understand the given expression. We have the expression (1-(1)/(x))/(1-(1)/(x^(2))). We need to simplify this expression by performing the operations in the numerator and the denominator.Simplify numerator: Simplify the numerator. The numerator is 1 - (1/x). To simplify this, we can find a common denominator, which is x. 1 - (1/x) = (x/x) - (1/x) = (x - 1)/xSimplify denominator: Simplify the denominator. The denominator is 1 - (1/x^2). To simplify this, we can find a common denominator, which is x^2. 1 - (1/x^2) = (x^2/x^2) - (1/x^2) = (x^2 - 1)/x^2Rewrite original expression: Rewrite the original expression with the simplified numerator and denominator. Now we have the expression with the simplified numerator and denominator: ((x - 1)/x) / ((x^2 - 1)/x^2)Divide fractions: Divide the fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. ((x - 1)/x) * (x^2/(x^2 - 1))Simplify expression: Simplify the expression. We notice that x in the numerator of the first fraction and x^2 in the numerator of the second fraction can be simplified. (x - 1)/x * x^2/(x^2 - 1) = (x - 1) * (x/x) * (x/(x^2 - 1)) = (x - 1) * (1) * (x/(x^2 - 1)) = (x - 1) * (x/(x^2 - 1))Factor denominator: Factor the denominator. The denominator x^2 - 1 is a difference of squares and can be factored as (x + 1)(x - 1). (x - 1) * (x/((x + 1)(x - 1)))Cancel common terms: Cancel out the common terms. We have (x - 1) in both the numerator and the denominator, so we can cancel them out. (x - 1) * (x/((x + 1)(x - 1))) = x/(x + 1)

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$\frac{1-\frac{1}{x}}{1-\frac{1}{x^{2}}}$

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Algebra 1

Multiplication with rational exponents

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\frac{1-\frac{1}{x}}{1-\frac{1}{x^{2}}}

Understand given expression: Understand the given expression. $\newline$ We have the expression $(1-\frac{1}{x})/(1-\frac{1}{x^2})$ . We need to simplify this expression by performing the operations in the numerator and the denominator.
Simplify numerator: Simplify the numerator. $\newline$ The numerator is $1 - (1/x)$ . To simplify this, we can find a common denominator, which is $x$ . $\newline$ $1 - (1/x) = (x/x) - (1/x) = (x - 1)/x$
Simplify denominator: Simplify the denominator. $\newline$ The denominator is $1 - (1/x^2)$ . To simplify this, we can find a common denominator, which is $x^2$ . $\newline$ $1 - (1/x^2) = (x^2/x^2) - (1/x^2) = (x^2 - 1)/x^2$
Rewrite original expression: Rewrite the original expression with the simplified numerator and denominator. $\newline$ Now we have the expression with the simplified numerator and denominator: $\newline$ $\frac{(x - 1)}{x}$ / $\frac{(x^2 - 1)}{x^2}$
Divide fractions: Divide the fractions. $\newline$ To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. $\newline$ $(\frac{x - 1}{x}) \times (\frac{x^2}{x^2 - 1})$
Simplify expression: Simplify the expression. $\newline$ We notice that $x$ in the numerator of the first fraction and $x^2$ in the numerator of the second fraction can be simplified. $\newline$ $\frac{x - 1}{x} \times \frac{x^2}{x^2 - 1} = (x - 1) \times \left(\frac{x}{x}\right) \times \left(\frac{x}{x^2 - 1}\right)$ $\newline$ $= (x - 1) \times (1) \times \left(\frac{x}{x^2 - 1}\right)$ $\newline$ $= (x - 1) \times \left(\frac{x}{x^2 - 1}\right)$
Factor denominator: Factor the denominator. $\newline$ The denominator $x^2 - 1$ is a difference of squares and can be factored as $(x + 1)(x - 1)$ . $\newline$ $(x - 1) * \left(\frac{x}{(x + 1)(x - 1)}\right)$
Cancel common terms: Cancel out the common terms. $\newline$ We have $(x - 1)$ in both the numerator and the denominator, so we can cancel them out. $\newline$ $(x - 1) \times \frac{x}{(x + 1)(x - 1)}$ = \frac{x}{x + $1$ }