Question

If 1/x-1-1/x+5= 6/7 where x is not equal to 1and -5 then x=

solve plz​

Answer 1

Answer:

x = - 6 or 2

Step-by-step explanation:

$\Rightarrow \sf \dfrac{1}{x - 1} - \dfrac{1}{x + 5} = \dfrac{6}{7}$

Multiplying every term with ( x - 1 )( x + 5 )

⇒ ( x + 5 ) - ( x - 1 ) = ( 6 / 7 )( x - 1 )( x + 5 )

⇒ x + 5 - x + 1 = ( 6 / 7 )[ x( x + 5 ) - 1( x + 5 ) ]

⇒ 6 = ( 6 / 7 )( x² + 5x - x - 5 )

⇒ 6 × ( 7 / 6 ) = x² + 4x - 5

⇒ 7 = x² + 4x - 5

⇒ 0 = x² + 4x - 5 - 7

⇒ 0 = x² + 4x - 12

⇒ x² + 4x - 12 = 0

Splitting the middle term

⇒ x² + 6x - 2x - 12 = 0

⇒ x( x + 6 ) - 2( x + 6 ) = 0

⇒ ( x + 6 )( x - 2 ) = 0

⇒ x + 6 = 0 or x - 2 = 0

⇒ x = - 6 or x = 2

Therefore the value of x is either - 6 or 2

Answer 2

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QUESTION :

If 1/x-1-1/x+5= 6/7 where x is not equal to 1and -5 then x=

If 1/x-1-1/x+5= 6/7 where x is not equal to 1and -5 then x=solve plz.

SOLUTION :

$\dfrac{1}{x - 1} - \dfrac{1}{x + 5} = \dfrac{6}{7}$

Now let us take LCM

=>

$\dfrac{6}{(x - 1)(x + 5)} = \dfrac{6}{7} \\ \\ = > 6( {x}^{2} + 4x - 5)= 42 \\ \\ = > 6 {x}^{2} + 24x - 72 = 0$

Factorising this expression ,

${x}^{2} + 4x - 12 = 0 \\ \\ = > {x}^{2} + 6x - 2x - 12 = 0 \\ \\ = > x(x +6 ) - 2(x + 6) = 0 \\ \\ = > (x - 2)(x + 6) = 0$

So,

X = 2 or -6

Answer :

X = 2 or -6