The expression given is,
[tex]\frac{2+3x}{16-81x^4}[/tex]
Rewrite the expression into the form of a²-b²
[tex]\frac{2+3x}{4^2-(9x^2)^2}[/tex]
Factor out the expression using
[tex]\begin{gathered} a^2-b^2=(a+b_)(a-b) \\ \therefore\frac{2+3x}{4^{2}-(9x^{2})^{2}}=\frac{2+3x}{(4+9x^2)(4-9x^2)} \end{gathered}[/tex]
Rewrite the expression into the form of a²-b²
[tex]\begin{gathered} (4-9x^2)=2^2-(3x)^2 \\ Factor\text{ the expression using} \\ a^2-b^2=(a+b)(a-b) \\ \frac{2+3x}{(4+9x^2)(4-9x^2)}=\frac{2+3x}{(4+9x^2)(2+3x)(2x-3)} \end{gathered}[/tex]
Cancel out the common factor (2+3x), we have
[tex]\frac{1}{(4+9x^2)(2-3x)}[/tex]
Hence, the equivalent expression is
[tex]\frac{1}{(4+9x^{2})(2-3x)}\text{ \lparen OPTION C\rparen}[/tex]
