Question

1/(x-2)-2/(x+4)=1/3
so what is x

Answer 1

Answer:

Required value of x is ( - 5 ± √153 ) / 2.

Step-by-step explanation:

Given equation is 1 / ( x - 2 ) - 2 / ( x + 4 ) = 1 / 3, we can't take the LCM directly, but we can multiply the terms( on numerator and denominator, both ) with the term in other fraction in the denominator.

= > 1 / ( x - 2 ) - 2 / ( x + 4 ) = 1 / 3

= > [ { 1 x ( x + 4 ) } / ( x - 2 )( x + 4 ) ] - [ { 2 x ( x - 2 ) } / { ( x + 4 ) ( x - 2 } ] = 1 / 3

= > ( x + 4 ) / ( x - 2 )( x + 4 ) - 2( x - 2 ) / ( x + 4 )( x - 2 ) = 1 / 3

Now, denominator of both the fractions is same.

= > { ( x + 4 ) - 2( x - 2 ) } / ( x + 4 )( x - 2 ) = 1 / 3

= > { x + 4 - 2x + 4 } / ( x + 4 ) ( x - 2 ) = 1 / 3

= > { 8 - x } / ( x + 4 )( x - 2 ) = 1 / 3

= > 3( 8 - x ) = ( x + 4 )( x - 2 )

= > 24 - 3x = x( x - 2 ) + 4( x - 2 )

= > 24 - 3x = x^2 - 2x + 4x - 8

= > 24 - 3x = x^2 + 2x - 8

= > x^2 + 2x + 3x - 8 - 24 = 0

= > x^2 + 5x - 32 = 0

By Quadratic Formula: -

x = { - b ± √( b^2 - 4ac ) } / 2a , where a and b are the coefficients of x^2 , x and the remaining value is cm on comparing the equation with ax^2 + bx + c = 0

Thus,

= > x = [ - 5 ± √{ ( 5 )^2 - 4( 1 x - 32 ) } ] / ( 2 x 1 )

= > x = [ - 5 ± √( 25 + 128 ) ] / 2

= > x = ( - 5 ± √153 ) / 2

Hence the required value of x is ( - 5 ± √153 ) / 2.