Question

solve for 'x' if (1/x+7) -(1/x+4) =5/6​

Answer 1

x−5)(x−7)(x+6)(x+4)=504{(x−5)(x+4)}{(x−7)(x+6)}=504(x2−x−20)(x2−x−42)=504

Put x2−x=t

(t−20)(t−42)=504t2−62t+840=504t2−62t+336=0t2−6t−56t+336=0t(t−6)−56(t−6)=0(t−56)(t−6)=0t=56,6x2−x=t

For t=56

x2−x=56x2−x−56=0x2−8x+7x−56=0x(x−8)+7(x−8)=0(x+7)(x−8)=0x=−7,8

 

For t=6

x2−x=6x2−x−6=0x2−3x+2x−6=0x(x−3)+2(x−3)=0(x+2)(x−3)=0x=−2,3

so the values of x are −7,8,−3 and 2

I HOPE IT'S HELPFUL FOR YOU