Question

1/x-3-1/x+5=1/6 solve using factorisation

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

Answer 2

Here is the your Answer dude
_________________________

1/(x-3) -1/(X+5) = 1/6

Take LCM (x-3) (X+5)
Now

(x+5)-(x-3) = [(X+5)(x-3)] /6
=>
X+5-x+3 = [x^2 -3x +5x -15 ] /6
=>
X^2+2x -15 = 8×6
X^2 +2x = 48+15
X^2 +2x -63=0
X^2+9x -7x -63 =0
X(X +9) -7(X+9) =0
(X+9) (x-7) Ans!

Hope it's helpful ✌