Question

solve for X 5/x^2-1 - 2/x = 2/x+1

Answer 1

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Answer 2

1. Make sure the denominators are factored:

\(\frac{5}{(x+1)(x-1)} - \frac{2}{x} = \frac{2}{x+1}\)

2. Multiply both sides by x-1 to get:

\(\frac{5}{x+1}- \frac{2x-2}{x} = \frac{2x-2}{x+1}\)

3. Add (2x-2)/x to both sides; subtract (2x-2)/(x+1) from both sides to get:
\(\frac{5}{x+1} - \frac{2x-2}{x+1} = \frac{2x-2}{x}\)

4. Combine fractions on the left side to get

\(\frac{7 - 2x}{x+1} = \frac{2(x-1)}{x}\)

5. Cross multiply to get:
\(x(7-2x) = 2(x+1)(x-1)\)

6. Simplify and Multiply to get
\(7x - 2x^2 = 2(x^2 -1)\)

7. Simplify further to get:

\(7x-2x^2 = 2x^2 - 2\)

Add 2x^2 to both sides; subtract 7x from both sides to get:
\(4x^2 - 7x - 2 = 0\)

Finish solving the quadratic equation.

Answer 3

Thanks