Question

Prove the algebraic identity with the left hand side and supplying a sequence of equivalent expressions that ends with the right hand side. X^3-x^2/x -(x-1)(x+1)=1-x

Answer 1

See Prove

Explanation:

Given the expression:
`(x^3-x^2)/(x) -(x-1)(x+1)`

To Prove:
`(x^3-x^2)/(x) -(x-1)(x+1)=1-x`

Taking the Left-Hand side

`(x^3-x^2)/(x) -(x-1)(x+1)\\=(x(x^2-x))/(x) -[x(x+1)-1(x+1)]\\=x^2-x-[x^2+x-x-1]\\=x^2-x-x^2+1\\=-x+1\\=1-x`

This is the right-hand side as required.

We have proved the given algebraic identity.