The simplest form of the given expression is [tex]\frac{1}{(x+1)(x-2)}[/tex].
What is Algebraic expression?
An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
Here, given expression;
[tex]\frac{x+2}{4x^2+5x+1} X \frac{4x+1}{x^2-4}[/tex]
[tex]\frac{x+2}{4x^2+4x +x+1} X \frac{4x+1}{x^2-2^2}[/tex]
[tex]\frac{x+2}{4x(x+1)+1(x+1)} X \frac{4x+1}{(x+2)(x-2)}[/tex]
[tex]\frac{x+2}{(4x+1)(x+1)} X \frac{4x+1}{(x+2)(x-2)}[/tex]
[tex]\frac{1}{(x+1)(x-2)}[/tex]
Thus, the simplest form of the given expression is [tex]\frac{1}{(x+1)(x-2)}[/tex].
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