Question

QuestionDetermine the value(s) for which the rational expressionlist them separated by a comma, e.g. n = 2,3.-3n + 12is undefined. If there's more than one value,84n2 + 76n +16

Answer 1

A rational expression is defined for all real numbers except the zeros of the denominator.

Then, find the zeros of the denominator to find the values for which the given rational expression is undefined:

`84n^2+76n+16=0`

Use quadratic formula:

`\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}`
`\begin{gathered} n=\frac{-76\pm\sqrt[]{76^2-4(84)(16)}}{2(84)} \\ \\ n=\frac{-76\pm\sqrt[]{5776-5376}}{168} \\ \\ n=\frac{-76\pm\sqrt[]{400}}{168} \\ \\ n=(-76\pm20)/(168) \\ \\ n_1=(-76+20)/(168)=(-56)/(168)=-(1)/(3) \\ \\ n_2=(-76-20)/(168)=(-96)/(168)=-(4)/(7) \end{gathered}`

Then, the given rational expression is undefined for:

n= -1/3 , -4/7