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Simplify $2x/x^2-1$ minus $1/1-x$

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Solve multi-step inequalities

Full solution

Q. Simplify

2x/x^2-1

minus

1/1-x

Factor Denominator: First, let's factor the denominator $x^2 - 1$ , which is a difference of squares. $\newline$ $x^2 - 1 = (x + 1)(x - 1)$
Rewrite Expression: Now, rewrite the expression with the factored denominator. $\frac{2x}{(x + 1)(x - 1)} - \frac{1}{1 - x}$
Rewrite Second Fraction: Notice that $1 - x$ is the same as $-(x - 1)$ . We can rewrite the second fraction as $-\frac{1}{x - 1}$ . $\newline$ $\frac{2x}{(x + 1)(x - 1)} - \left(-\frac{1}{x - 1}\right)$
Combine Fractions: Now, we have a common denominator of $(x + 1)(x - 1)$ for the first term and $(x - 1)$ for the second term. We can combine the fractions. $\frac{2x - (-1)}{(x + 1)(x - 1)}$
Simplify Numerator: Simplify the numerator. $\newline$ $(2x + 1)/(x + 1)(x - 1)$
Final Simplified Form: Now, we check for any further simplifications. The numerator and denominator have no common factors, so this is the final simplified form.

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