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

Answer:

See Prove

Step-by-step explanation:

Given the expression: $\dfrac{x^3-x^2}{x} -(x-1)(x+1)$

To Prove: $\dfrac{x^3-x^2}{x} -(x-1)(x+1)=1-x$

Taking the Left-Hand side

$\dfrac{x^3-x^2}{x} -(x-1)(x+1)\\=\dfrac{x(x^2-x)}{x} -[x(x+1)-1(x+1)]\\=x^2-x-[x^2+x-x-1]\\=x^2-x-x^2+1\\=-x+1\\=1-x$

This is the right-hand side as required.

We have proved the given algebraic identity.