To simplify the expression \( \frac{x + 5x + 6}{x + 2} \), we start by combining like terms in the numerator.
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Combine the \( x \) terms: \[ x + 5x = 6x \] So, the expression becomes: \[ \frac{6x + 6}{x + 2} \]
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Now, factor the numerator: \[ 6x + 6 = 6(x + 1) \]
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This allows us to rewrite the expression: \[ \frac{6(x + 1)}{x + 2} \]
The expression is now in a simpler form, but it cannot be simplified further by canceling, since \( x + 1 \) and \( x + 2 \) have no common factors.
Thus, the simplified expression in standard form is: \[ \frac{6(x + 1)}{x + 2} \]
Or, if you prefer to leave it as a completely simplified rational expression, it can be expressed as: \[ \frac{6x + 6}{x + 2} \]
This represents the simplified form of the original expression.