Urgent!

Question

Create a rational expression in the form ax²-bx+c over dx²+ex+f that has non permissible values x≠2 and x≠-9

Answer 1

Given Rational expression is ( ax²-bx+c ) / ( dx²+ex+f )

Non permissible values  are  x≠2 and x≠-9

Non-permissible values are roots of the denominator.

Non permissible values are 2 , -9. So denominator is (x – 2)( x – (-9))

= (x – 2 ) (x + 9)

=  x (x + 9) – 2(x + 9)

= x² + 9x – 2x - 18

=  x² + 7x - 18

But Denominator is dx² + ex + f.So substitute denominator as x² + 7x - 18.

Hence Rational expression is ( ax²-bx+c ) / (x² + 7x - 18 ).