Question

Simplify the rational expression below. When typing your numerator and denominators be sure to but the term with the variable first and do not put spaces between your characters. \frac{\left(12n^2-29n-8\right)}{\left(28n^2-5n-3\right)} The numerator is AnswerThe denominator is Answer

Answer 1

Given the rational expression below:

`(12n^2-29n-8)/(28n^2-5n-3)`

The simplification is as shown below:

`\begin{gathered} (12n^2-29n-8)/(28n^2-5n-3)=(12n^2-32n+3n-8)/(28n^2-12n+7n-3) \\ (12n^2-32n+3n-8)/(28n^2-12n+7n-3)=(4n(3n-8)+1(3n-8))/(4n(7n-3)+1(7n-3)) \\ (4n(3n-8)+1(3n-8))/(4n(7n-3)+1(7n-3))=((3n-8)(4n+1))/((7n-3)(4n+1)) \end{gathered}`

It can be observed from the simplification that (4n+1) is common to both the numerator and denominator. To simplify further we will cross (4n+1) out in the numerator and denominator as shown below:

`\begin{gathered} ((3n-8)(4n+1))/((7n-3)(4n+1))=(3n-8)/(7n-3) \\ Hence,(12n^2-29n-8)/(28n^2-5n-3)=(3n-8)/(7n-3) \end{gathered}`

Hence, after the simplification,

the numerator is 3n - 8, and

The denominator is 7n - 3