Math, asked by AsifAhamed4, 1 year ago

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

Answers

Answered by Anonymous
35

 \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 \green{ \boxed{ \boxed{ \mathbb{THANKS}}}}



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

Anonymous: ☺.
Anonymous: ✌.
siddhartharao77: nice explanation!
Anonymous: thanks
arti44: Hey ur ans is impressive
arti44: I will not ask u how u write this because i know u will not explained us .
Anonymous: :-)
Answered by Anonymous
12
hey mate
here's the solution
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1navya: nyc ans
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