Question

Solve the following quadratic equation by factorization method

1/a+b+x = 1/a + 1/b +1/x , a and b is not equal to zero

Answer 1

1/(a+b+x)=1/a + 1/b + 1/x
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