Answer:
Factorise both sides of
ax+bx=a2−b2
and get
(a+b)x=(a+b)(a−b).
If
a+b≠0,
because division by 0 is not allowed, then divide by a + b and get
(a+b)xa+b=(a+b)(a−b)a+b.
It reduces to
x=a−b.
If a+b=0, then
ax+bx=a2−b2 is
(a+b)x=(a+b)(a−b)
and this simplifies to
0x=0(a−b),
that is,
0=0,
so that the value of x is indeterminate.
