Question

Determine the value(s) for which the rational expression -3n+12/84n² +76n +16 is undefined.

Answer 1

Given rational expression is

`(-3n+12)/(84n^2+76n+16)`

Find:

We have to find the value of n for which rational expression is undefined.

Step-by-step explanation:

`\begin{gathered} (-3n+12)/(84n^(^2)+76n+16)=(-3n+12)/(4(21n^2+19n+4)) \\ =(-3n+12)/(4(21n^2+7n+12n+4)) \\ =(-3n+12)/(4(7n(3n+1)+4(3n+1))) \\ =(-3n+12)/(4(3n+1)(7n+4)) \end{gathered}`

Now, the given expression is undefined, when denominator is equal to zero.

i.e. when

4 (3n+1)(7n+4)=0,

when , (3n+1)(7n+4)=0

when,

either (3n+1)=0 or (7n+4)=0

when,

n= -1/3 or n= -4/7.

Therefore, the given expression is undefined for n = -1/3 or n = - 4/7.