Rational expressions and equations simplify, state the non-premissible value(s)

Question

1. 2x+12/(x+6)(2x+1)
2. 14-2n/n²-7n
3. 6y²+9y/12y²

 

 

Simplify . State the non-permissible value

Answer 1

1)     2x+12/(x+6)(2x+1)

 

1st - determine non-permissible values       

Take the denominator and make it equal zero
         (x+6)(2x+1)=0

        x+6=0  ; 2x+1 = 0

         x= -6   ; 2x =-1

                    ; x=-1/2 

 

Non-permissible values are x ≠ -6, -1/2

2nd - look to cancel out equivalent expression 

 

     2(x+6)/(x+6)(2x+1)

     2(x+6)/(x+6)(2x+1)

             2/(2x+1) 

 

Final answer : 2/(2x+1) ; x ≠ -6, -1/2

 

2)  14-2n/n²-7n

 

1st - determine non-permissible values
Take the denominator and make it equal zero
    n²-7n = 0

  n(n-7) = 0

n=0  ; n-7 = 0

        ; n=7

Non-permissible values are n ≠ 0, 7
2nd - look to cancel out equivalent expression

 

       14-2n/n²-7n

    2 (7-n) /n (n-7)

   - 2 (n-7) /n (n-7)

- 2 (n-7) /n  (n-7)

         -2/n  

 

Final answer : -2/n ; n ≠ 0, 7

 

3)  6y²+9y/12y²

1st - determine non-permissible values
Take the denominator and make it equal zero

 12y² = 0

     y² = 0

      y = 0

Non-permissible values are y ≠ 0
2nd - look to cancel out equivalent expression

   

     6y²+9y/12y²  

 

    3y(2y+3)/3* 4 y²

 

    3 y(2y+3)/3* 4 y* y

 

      (2y+3)/4y  

 

Final answer :  (2y+3)/4y ;  y ≠ 0