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Here is your solution....☺
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Hope this helps you...☺
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see it is given that.. 1/x+2 + 1/x = 3/4
so on taking lcm.. we get
x + x + 2/x^2 + 2x = 3/4
so 4 (2x + 2) = 3 ( x^2 + 2x )
8x + 8 = 3x^2 + 6x
on transposing we get
3x^2 + 6x - 8x - 8 = 0
3x^2 - 2x - 8 = 0
on middle term splitting we get
3x^2 - 6x + 4x - 8 = 0
so 3x ( x - 2 ) + 4 ( x - 2 ) = 0
( x - 2 ) ( 3x + 4 ) = 0
so in first case...
x - 2 =0
so x = 2.
in second case...
3x + 4 = 0
3x = - 4
x = -4/3
therefore x = 2 , -4/3
so on taking lcm.. we get
x + x + 2/x^2 + 2x = 3/4
so 4 (2x + 2) = 3 ( x^2 + 2x )
8x + 8 = 3x^2 + 6x
on transposing we get
3x^2 + 6x - 8x - 8 = 0
3x^2 - 2x - 8 = 0
on middle term splitting we get
3x^2 - 6x + 4x - 8 = 0
so 3x ( x - 2 ) + 4 ( x - 2 ) = 0
( x - 2 ) ( 3x + 4 ) = 0
so in first case...
x - 2 =0
so x = 2.
in second case...
3x + 4 = 0
3x = - 4
x = -4/3
therefore x = 2 , -4/3
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