Question

Okay that’s okay I’m not taking it out there for the day

Answer 1

The expression given is,

`(2+3x)/(16-81x^4)`

Rewrite the expression into the form of a²-b²

`(2+3x)/(4^2-(9x^2)^2)`

Factor out the expression using

`\begin{gathered} a^2-b^2=(a+b_)(a-b) \\ \therefore(2+3x)/(4^(2)-(9x^(2))^(2))=(2+3x)/((4+9x^2)(4-9x^2)) \end{gathered}`

Rewrite the expression into the form of a²-b²

`\begin{gathered} (4-9x^2)=2^2-(3x)^2 \\ Factor\text{ the expression using} \\ a^2-b^2=(a+b)(a-b) \\ (2+3x)/((4+9x^2)(4-9x^2))=(2+3x)/((4+9x^2)(2+3x)(2x-3)) \end{gathered}`

Cancel out the common factor (2+3x), we have

`(1)/((4+9x^2)(2-3x))`

Hence, the equivalent expression is

`(1)/((4+9x^(2))(2-3x))\text{ \lparen OPTION C\rparen}`