To add the polynomials \( (4x^2 - x + 5) + (5x^2 + x + 9) \), you combine like terms.
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Combine the \( x^2 \) terms: \[ 4x^2 + 5x^2 = 9x^2 \]
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Combine the \( x \) terms: \[ -x + x = 0 \]
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Combine the constant terms: \[ 5 + 9 = 14 \]
Putting it all together, the resulting polynomial is: \[ 9x^2 + 0x + 14 \]
Since the term \( 0x \) can be omitted, the final answer in standard form is: \[ 9x^2 + 14 \]