Question

How are these two equations related? (x^2-1)/(x+1)= x-1 and x^2-1=(x+1)(x-1)

Answer 1

These two equations are related to each other by identity
`a^2-b^2=(a+b)(a-b)`

Explanation:

We have given equations

`(x^2-1)/(x+1)`

We know the algebraic identity

`a^2-b^2=(a+b)(a-b)`

So
`a^2-1^2=(x+1)(x-1)`

So
`(x^2-1)/(x+1)=((x+1)(x-1))/(x+1)=(x-1)`

So these two equations are related to each other by algebraic identity
`a^2-b^2=(a+b)(a-b)`