I need help please :(

Question

Please state all the non permissible  rational expressiom.

a) 2x+1 over x-2

b) 7x over x²-16

c) 5x+3 over x²+9x+20

d) 4x+9 over 3x²-12x-36

e) 3x-8 over x²+5x

f) 9x-2 over x²+8

g) 8x+12 over x³-25x

h) 6x-7 over 5(x-2)(x+6)

Thanks! Urgent :(

Answer 1

a)

( 2x+1 ) / ( x-2 )

To determine non-permissible values.Take the denominator and make it equal to zero.

Denominator = 0  ⇒   x - 2 = 0   ⇒   x = 2.

Given rational expression is undefined at x = 2.

Hence , non-permissible value : x = 2.

Answer 2

b)

( 7x) / ( x²-16 )

To determine Non-permissible values. Take the denominator and make it equal to zero.

Denominator = 0  ⇒   x² - 16 = 0 ⇒   x² = 16  ⇒   x = √16   ⇒   x = ± 4

Given rational expression is undefined at x = - 4  and 4 .

Hence , non-permissible values : x = 4 , - 4.

Answer 3

c)

( 5x + 3) / ( x² + 9x + 20 )

To determine Non-permissible values.Take the denominator and make it equal to zero.

Denominator = 0  ⇒   x² + 9x + 20 = 0 ⇒   x² + 5x + 4x + 20 = 0

⇒   x(x + 5) + 4(x + 5) = 0    ⇒  (x + 4)(x + 5) = 0

⇒ (x + 4) = 0 ; (x + 5) = 0

⇒ x = - 4  ; x = - 5.

Given rational expression is undefined at x = - 4  and – 5.

Non-permissible values : x = - 4 , - 5.

Answer 4

d)

( 4x+9 ) / ( 3x²-12x-36 )

To determine Non-permissible values. Take the denominator and make it equal to zero.

Denominator = 0  ⇒   3x² - 12x - 36 = 0   ⇒  3 ( x² - 4x – 12 ) = 0  ⇒  x² –  4x – 12  = 0

⇒   x² - 6x + 2x - 36 = 0   ⇒   x(x - 6) + 2(x - 6) = 0    ⇒   (x - 6)(x + 2) = 0

⇒  (x - 6) = 0 ; (x + 2) = 0

⇒  x = 6  ; x = - 2.

Given rational expression is undefined at x = 6  and – 2.

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

Answer 5

e)

( 3x - 8 ) / ( x² + 5x )

To determine Non-permissible values. Take the denominator and make it equal to zero.

Denominator = 0  ⇒   x² + 5x = 0   ⇒  x ( x + 5 ) = 0

⇒  x = 0 ; (x + 5) = 0

⇒  x = 0  ; x = - 5.

Given rational expression is undefined at x = 0  and – 5.

Hence , Non-permissible values : x = 0 ,– 5.

Answer 6

g)

( 3x - 8 ) / ( x³ - 25x )

To determine Non-permissible values. Take the denominator and make it equal to zero.

Denominator = 0  ⇒   x² - 25x = 0   ⇒  x ( x² - 25 ) = 0

⇒  x = 0 ; (x² - 25) = 0

⇒  x = 0  ; x² = 25.

⇒  x = 0  ; x = 5  ;  x = -5.                   (   x² = 25  ⇒  x = √25  ⇒  x = ± 5 )

Given rational expression is undefined at x = 0  5 and -5.

Hence , Non-permissible values : x = 0 , 5 , - 5.

Answer 7

h)

( 6x - 7) / ( 5(x-2)(x+6) )

To determine Non-permissible values.Take the denominator and make it equal to zero.

Denominator = 0  ⇒   5(x-2)(x+6) = 0 ⇒  (x - 2)(x + 6) = 0

⇒ (x - 2) = 0 ; (x + 6) = 0

⇒ x = 2  ; x = - 6.

Given rational expression is undefined at x = 2  and – 6.

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

Answer 8

f)

( 9x - 2 ) / ( x² + 8 )

To determine Non-permissible values. Take the denominator and make it equal to zero.

Denominator = 0  ⇒   x² + 8 = 0 ⇒   x² = - 8   ⇒   x = √(-8)

x is imaginary value.

Hence , Given rational expression does not have Non-permissible values.