Question

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

Answer 1

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….

Answer 2

Solution:-

given by:-
$\frac{x + 2}{ {x}^{2} + 3x + 2} + \frac{x - 3}{ {x}^{2} - 2x - 3} \\ \frac{(x + 2)}{ {x}^{2} + 2x + x + 2 } + \frac{(x - 3)}{ {x}^{2} - 3x + x - 3} \\ \frac{(x + 2)}{x(x + 2) + 1(x + 2)} + \frac{(x - 3)}{(x - 3)(x - 1)} \\ \frac{(x + 2)}{(x + 2)(x + 1)} +\frac{(x - 3)}{(x - 3)(x + 1)} \\ \frac{1}{(x + 1)} +\frac{1}{(x + 1)}\\\frac{2}{(x + 1)}\: ans$
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