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

Here ,
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we used algebraic identity :

a² - b² = ( a + b )( a - b )
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x² - 1

= x² - 1²

= ( x + 1 )( x - 1 )

Required quotient = 2/( x + 1 )

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