Question

If ax+bx=a^2-b^2 then what is the value of x​

Answer 1

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.