Question

Using factorization solve the quadratic equation :

$\frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} = \frac{5}{6}$

Where x is not equal to - 1 and 1

Answer 1

$\huge \bf \red{Hey \: there !! }$




$\frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} = \frac{5}{6} . \\ \\ = > \frac{ {(x + 1)}^{2} - {(x - 1)}^{2} }{(x - 1)(x + 1)} = \frac{5}{6} . \\ \\ = > \frac{ {x}^{2} + 1 + 2x - ( {x}^{2} + 1 - 2x) }{ {x}^{2} - 1} = \frac{5}{6} . \\ \\ = > \frac{ \cancel{{x}^{2}} + \cancel1 + 2x - \cancel{{x}^{2}} - \cancel1 + 2x }{ {x}^{2} - 1} = \frac{5}{6} . \\ \\ = > \frac{4x}{ {x}^{2} - 1 } = \frac{5}{6} . \\ \\ = > 6(4x) = 5( {x}^{2} - 1). \\ \\ = > 24x = 5 {x}^{2} - 5. \\ \\ = > 5 {x}^{2} - 24x - 5 = 0. \\ \\ = > 5 {x}^{2} - 25x + x - 5 = 0. \\ \\ = > 5x(x - 5) + 1(x - 5) = 0. \\ \\ = > (5x + 1)(x - 5) = 0. \\ \\ = > 5x + 1 = 0. \: \: or \: \: x - 5 = 0. \\ \\ \boxed { \blue{ \bf \therefore x = \frac{ - 1}{5} . \: \: or \: \: x = 5 }}$



✔✔ Hence, it is solved ✅✅.

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$\huge \bf \purple{ \#BeBrainly.}$

Answer 2

hey mate
here's the solution