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Maths-

General

Easy

Question

$fraction numerator x plus 2 over denominator left parenthesis x plus 2 right parenthesis to the power of 2 end exponent end fraction$
Which of the following expressions is equivalent to the given expression, where $x not equal to negative 2$ ?

$x + 2$
$\frac{1}{x + 2}$
$x^{2} + 2 x + 4$
$\frac{1}{x^{2} + 2 x + 4}$

The correct answer is: $fraction numerator 1 over denominator x plus 2 end fraction$

We know that- x² = x × x
∴ (x + 2)² in the given question can be expanded as (x + 2) × (x + 2)
Step-by-step solution:-
$fraction numerator x plus 2 over denominator left parenthesis x plus 2 right parenthesis to the power of 2 end exponent end fraction equals fraction numerator x plus 2 over denominator open parentheses x plus 2 close parentheses open parentheses x plus 2 close parentheses end fraction$
$equals fraction numerator left parenthesis x blank plus blank 2 right parenthesis over denominator left parenthesis x blank plus blank 2 right parenthesis left parenthesis x plus 2 right parenthesis end fraction$
$equals fraction numerator 1 over denominator x plus 2 end fraction$
Final Answer:-
Option B i.e. $fraction numerator 1 over denominator X plus 2 end fraction$ is the correct Option.

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