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Sagot :
Given rational expression is
[tex]\frac{-3n+12}{84n^2+76n+16}[/tex]Find:
We have to find the value of n for which rational expression is undefined.
Explanation:
[tex]\begin{gathered} \frac{-3n+12}{84n^{^2}+76n+16}=\frac{-3n+12}{4(21n^2+19n+4)} \\ =\frac{-3n+12}{4(21n^2+7n+12n+4)} \\ =\frac{-3n+12}{4(7n(3n+1)+4(3n+1))} \\ =\frac{-3n+12}{4(3n+1)(7n+4)} \end{gathered}[/tex]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.
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