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 :

i ) x² - 4

= x² - 2²

= ( x + 2 )( x - 2 ) -------( 1 )
_______________________

ii ) x² + 6x + 8

= x² + 2x + 4x + 8

= x( x + 2 ) + 4( x + 2 )

= ( x + 2 )( x + 4 ) -----( 2 )
_______________________

iii ) x² - 11x + 30

= x² - 5x - 6x + 30

= x( x - 5 ) - 6( x - 5 )

= ( x - 5 )( x - 6 ) --------( 3 )
______________________

iv ) x² - x - 20

= x² - 5x + 4x - 20

= x( x - 5 ) + 4( x - 5 )

= ( x - 5 )( x + 4 ) ----( 4 )
________________________

Now ,

[( x²-4)/(x²+6x+8) ]-[(x²-11x+30)/(x²-x-20)]

=[(x+2)(x-2)/(x+2)(x+4)]-[(x-5)(x-6)/(x-5)(x+4)]

= [ (x2)/(x+4) ] - [ (x-6)/(x+4)]

= [ x - 4 - ( x - 6 ) ]/( x + 4 )

= ( x - 4 - x + 6 )/( x + 4 )

= 2 /( x + 4 )

••••