Questions: Add. [ frac2 x^22 x+1+frac9 x+42 x+1= ]

$Add. [ frac2 x^22 x+1+frac9 x+42 x+1= ]$

Transcript text: Add. \[ \frac{2 x^{2}}{2 x+1}+\frac{9 x+4}{2 x+1}= \]

Solution

Solution Steps

To add the given fractions, we notice that they have a common denominator. Therefore, we can directly add the numerators and keep the common denominator.

Step 1: Identify the Common Denominator

The given fractions have a common denominator: \[ \frac{2x^2}{2x+1} + \frac{9x+4}{2x+1} \]

Step 2: Combine the Numerators

Since the denominators are the same, we can add the numerators directly: \[ \frac{2x^2 + (9x + 4)}{2x + 1} = \frac{2x^2 + 9x + 4}{2x + 1} \]

Step 3: Simplify the Resulting Fraction

We simplify the fraction: \[ \frac{2x^2 + 9x + 4}{2x + 1} \] By performing polynomial division or factoring, we find that: \[ \frac{2x^2 + 9x + 4}{2x + 1} = x + 4 \]

Final Answer

$\boxed{\frac{2x^2 + 9x + 4}{2x + 1}}$

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