The equivalent expression is:
[tex]\frac{x + 9}{2 + x} [/tex]
Option C is correct
The given expression is:
[tex] \frac{(x + 9)(x - 2)}{(x - 2)(2 + x)} [/tex]
By carefully observing the numerator and denominator of the given fractional expression, x-2 is common to both the numerator and denominator.
This common term can cancel out.
Therefore, the resulting expression is:
[tex] \frac{x + 9}{2 + x} [/tex]
In conclusion, the expression that is equal to
[tex]\frac{(x + 9)(x - 2)}{(x - 2)(2 + x)}[/tex]
is
[tex]\frac{x + 9}{2 + x} [/tex]
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