Questions: Add. 4/x + 3/(x+6) Simplify your answer as much as possible.

Transcript text: Add. \[ \frac{4}{x}+\frac{3}{x+6} \] Simplify your answer as much as possible.

Solution

Solution Steps

Step 1: Define the Rational Expressions

We start with the two rational expressions: \[ \frac{4}{x} \quad \text{and} \quad \frac{3}{x+6} \]

Step 2: Find the Common Denominator

The common denominator for the two fractions is: \[ x(x + 6) \]

Step 3: Rewrite Each Fraction with the Common Denominator

We rewrite each fraction to have the common denominator: \[ \frac{4}{x} = \frac{4(x + 6)}{x(x + 6)} = \frac{4x + 24}{x(x + 6)} \] \[ \frac{3}{x + 6} = \frac{3x}{x(x + 6)} \]

Step 4: Add the Fractions

Now we can add the two fractions: \[ \frac{4x + 24}{x(x + 6)} + \frac{3x}{x(x + 6)} = \frac{4x + 24 + 3x}{x(x + 6)} = \frac{7x + 24}{x(x + 6)} \]

Step 5: Simplify the Result

The final simplified result of the addition is: \[ \frac{7x + 24}{x(x + 6)} \]

Final Answer

\(\boxed{\frac{7x + 24}{x(x + 6)}}\)

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