Question

(1/x-3)-(1/x+5)=1/6, where x not equals to 3,-5

Answer 1

1/x-3 - 1/x+5 =1/6

taking LCM

x+5-(x-3) whole divided by (x-3)(x+5)=1/6

x+5-x+3 whole divided by x2+5x-3x-15=1/6

8/x2 +2x-15=1/6

BY cross multiplication:

x2+2x-15=48

=> x2+2x -15-48=0

=> x2+2x-63=0

=> x2+9x-7x-63= 0

=> x(x+9)-7(x+9)=0

=>(x+9)(x-7)= 0

=>x+9=0  => x=-9

x-7=0  => x=7

hence x= 7 or -9