QuestionJuly 20, 2025

Solve. (x)/(x-1)-(5)/(x+1)=(2)/(x^2)-1 x=square (Simplify your answer.including any radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Solve. (x)/(x-1)-(5)/(x+1)=(2)/(x^2)-1 x=square (Simplify your answer.including any radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Solve.
(x)/(x-1)-(5)/(x+1)=(2)/(x^2)-1
x=square 
(Simplify your answer.including any radicals and i as needed. Use integers or fractions for
any numbers in the expression. Use a comma to separate answers as needed.)

Solution
4.7(199 votes)

Answer

3, 1 Explanation 1. Simplify the equation Recognize that x^2 - 1 = (x-1)(x+1). Rewrite the equation as \frac{x(x+1) - 5(x-1)}{(x-1)(x+1)} = \frac{2}{(x-1)(x+1)}. 2. Combine and simplify the numerator Simplify the numerator: x(x+1) - 5(x-1) = x^2 + x - 5x + 5 = x^2 - 4x + 5. 3. Set numerators equal Since denominators are equal, set x^2 - 4x + 5 = 2. 4. Solve the quadratic equation Rearrange to x^2 - 4x + 3 = 0. Factor as (x-3)(x-1) = 0. 5. Find solutions Solve for x: x = 3 or x = 1.

Explanation

1. Simplify the equation<br /> Recognize that $x^2 - 1 = (x-1)(x+1)$. Rewrite the equation as $\frac{x(x+1) - 5(x-1)}{(x-1)(x+1)} = \frac{2}{(x-1)(x+1)}$.<br />2. Combine and simplify the numerator<br /> Simplify the numerator: $x(x+1) - 5(x-1) = x^2 + x - 5x + 5 = x^2 - 4x + 5$.<br />3. Set numerators equal<br /> Since denominators are equal, set $x^2 - 4x + 5 = 2$.<br />4. Solve the quadratic equation<br /> Rearrange to $x^2 - 4x + 3 = 0$. Factor as $(x-3)(x-1) = 0$.<br />5. Find solutions<br /> Solve for $x$: $x = 3$ or $x = 1$.
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