Question

show that (12/x+2)+(10/x-1)=7/2 can be simplified to give the equation 7x^2-37x-30=0

Answer 1

Solution :

12/(x+2 ) + 10/(x-1) = 7/2

= [ 12(x-1)+10(x+2) ]/[(x+2)(x-1) ] = 7/2

= [ 12x - 12+10x+20 ]/[x²-x+2x-2 ] = 7/2

=> (22x + 8)/( x² + x - 2 ) = 7/2

=>[ 2( 11x + 4 )] /( x² + x - 2 ) = 7/2

=> ( 11x + 4 ) = 7( x² + x - 2 )

=> 11x + 4 = 7x² + 7x - 14

=> 0 = 7x² + 7x - 14 - 11x - 4

=> 7x² - 18x - 4 = 0

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