Question

solve 1/a+b+x=1/a+1/b+1/x,a+b is not equal to 0​

Answer 1

1/(a+b+x)=(bx+ax+ab)/abx

abx=abx+a2x+a2b+b2x+abx+ab2+bx2+ax2+abx

ax2+bx2+a2x+abx+abx+b2x+a2b+ab2=0

x2(a+b)+ax(a+b)+bx(a+b)+ab(a+b)=0

(a+b)(x2+ax+bx+ab)=0

since, a+b!=0

so, x2+ax+bx+ab=0

x(x+a)+b(x+a)=0

(x+a)(x+b)=0

x=-a,-b