Help please :(

Question

What are the non permissible for each of the following rational.

a) 7x²-5x+18 over x-6 * 4x²-25 over x²+11x+28

b) x²+14x+33 over 2x²-98 divided by x-5 over (x+3)(x-7)

Answer 1

a)

Given rational function

 

Non-permissible values are values that make the denominator zero.

Denominator = 0  ⇒  ( x – 6 ) ( 4x² - 25 ) = 0

⇒ ( x – 6 ) ( (2x)² - 5² ) = 0

⇒ ( x – 6 ) ( 2x - 5 ) (2x + 5 ) = 0

( x – 6 ) = 0  ; ( 2x - 5 ) = 0  ;  (2x + 5 ) = 0

x = 6   ;   2x – 5 = 0   ;   2x + 5  = 0

x = 6   ;   x = 5/2 = 0   ;   x = - 5/2

Given rational expression is undefined at x = 6 , 5/2 and -5/2 .

Hence , Non-permissible values : x = 6 , 5/2 , -5/2.

Answer 2

b)

Given rational function

 

Non-permissible values are values that make the denominator zero.

Denominator = 0  ⇒  ( 2x² - 98 ) ( x – 5 ) = 0

⇒ 2 ( x² - 49 ) ( x – 5 )  = 0

⇒ ( x² - 49 ) ( x – 5 )  = 0

⇒ ( x² - 7² ) ( x – 5 )  = 0

⇒ ( x - 7 ) ( x + 7 ) ( x – 5 )  = 0

 

( x – 7 ) = 0  ;  ( x + 7 ) = 0  ; ( x - 5 ) = 0

x = 7   ;   x = -7   ;   x = 5

Given rational expression is undefined at x = 5 , 7 and -7 .

Hence , Non-permissible values : x = 5 , 7 , -7.