Question

1. Simplify the following as a quotient of two polynomials in the simplest form.

Answer 1

HELLO DEAR,

$\mathbf{\frac{x^3}{x-2} + \frac{8}{2 - x}}\\ \\ \mathbf{\frac{x^3}{x - 2}-\frac{8}{x - 2}}\\ \\ \mathbf{\frac{x^3 - 2^3}{x - 2}}\\ \\ \mathbf{\frac{(x - 2)(x^2 + 4 + 2x)}{(x - 2)}} \\ \\ \mathbf{(x^2 + 2x + 4)}$

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

SOLUTION IS IN THE ATTACHMENT

RATIONAL EXPRESSIONS :
A rational number is defined as a quotient a/b, of two integers a and b and b ≠0.A rational expression is a quotient p(x) /q(x) of two Polynomials p(x) and q(x) ,where q(x) ≠0.
•When the numerator and denominator of a rational expression do not have any common factor except 1, the rational expression is said to be expressed in the lowest terms.
•To reduce a rational expression to the lowest terms, factorise the numerator and the denominator and cancel the factors which are common to both.

HOPE THIS WILL HELP YOU….