Solve 6x 8x 5 3SolutionGiven that 6 x 8 x5 3 6x

Solution

Given that

( 6 / x ) + ( 8 / x+5 ) = 3

[ 6(x + 5) + 8x ] / x(x+5) = 3

6x + 30 + 8x = 3 [  x(x+5) ]

14x + 30 = 3 ( x² + 5x )

14x + 30 = 3x² + 15x

3x² + 15x -14x - 30 = 0

3x² + x - 30 = 0

3x² +10x - 9x -30 = 0

x (3x + 10 ) - 3 ( 3x + 10) = 0

   (3x + 10 ) (x - 3) = 0

3x + 10 = 0 ,x - 3 = 0

x = -10/3 , x = 3

Therefore,

The values of x = 3 , -10/3