Question

If (x+2/x-2) - (x-2/x+2) = (x-1/x+3) - (x+3/x-3) then the values of X are

Please Give Full Solution

(d) None is Correct Answer
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Answer 1

Given -

$\displaystyle \sf{ \bold { \dfrac { x + 2 }{ x - 2 } - \dfrac{ x - 2 }{ x + 2 } = \dfrac { x - 1 }{ x + 3 } - \dfrac{ x + 3 }{ x - 3 } }} \\ \\ \sf{ \bold { \implies { \dfrac{ (x - 2)(x + 2) - (x - 2)( x - 2) }{ ( x - 2 )( x + 2 ) } = \dfrac{ (x - 1 )( x - 3 ) - ( x + 3)( x + 3 ) }{ (x + 3)( x - 3 ) } }}}$

$\sf{ \bold { \implies { \dfrac{ x^2 - 4 - ( x^2 - 2x + 4 ) }{ x^2 - 4 } = \dfrac{ x^2 - 4x + 3 - ( x^2 - 6x + 3 ) }{ x^2 - 9 } }}} \\ \\ \sf{ \bold { \implies { \dfrac{ x^2 - 4 - x^2 + 2x - 4 }{ x^2 - 4 } = \dfrac{ x^2 - 4x + 3 - x^2 + 6x - 3 }{ x^2 - 9 } }}}$

$\sf{ \bold { \implies { \dfrac{ 2x - 8 }{ x^2 - 4 } = \dfrac{ 2x }{ x^2 - 9 } }}} \\ \\ \sf{ \bold { \implies { 2x ( x^2 - 4 ) = ( 2x - 8 )(x^2 - 9 ) }}} \\ \\ \sf{ \bold { \implies { 2x^3 - 8x = 2x^3 - 18x - 8x^2 + 72 }}}$

$\sf{ \bold { \implies { 8x^2 + 10x - 72 = 0 }}} \\ \\ \sf{ \implies { \bold { 4x^2 + 5x - 36 = 0 }}} \\ \\ \sf{ \bold { \implies { x = \dfrac{ -b \pm \sqrt{ b^2 - 4ac } }{ 2a } }}}$

$\sf{ \bold { \implies { x = \dfrac{ -5 \pm \sqrt{ 25 \pm 24.5 } }{ 8 } }}} \\ \\ \sf{ \bold { \implies { Thus, \: the \: answer \: isn't \: in \: terms \: of square \: roots . }}}$

$\sf{ \bold { \implies { Option \: D \: is \: the \: correct \: answer \: . }}}$