Rationalise the denominator of `(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))`.

Explanation

To rationalize the denominator of the expression \(\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}\), we can follow these steps:

### Step 1: Multiply by the Conjugate
To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of \(\sqrt{3} - \sqrt{2}\) is \(\sqrt{3} + \sqrt{2}\).

\[ \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} \cdot \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}} = \frac{(\sqrt{3} + \sqrt{2})^2}{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})} \]

### Step 2: Expand the Numerator
Now we expand the numerator using the formula \((a + b)^2 = a^2 + 2ab + b^2\):

\[ (\sqrt{3} + \sqrt{2})^2 = (\sqrt{3})^2 + 2(\sqrt{3})(\sqrt{2}) + (\sqrt{2})^2 = 3 + 2\sqrt{6} + 2 = 5 + 2\sqrt{6} \]

### Step 3: Expand the Denominator
Next, we expand the denominator using the difference of squares formula \(a^2 - b^2\):

\[ (\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}) = (\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1 \]

### Step 4: Combine Results
Now we can combine the results from the numerator and denominator:

\[ \frac{5 + 2\sqrt{6}}{1} = 5 + 2\sqrt{6} \]

### Final Answer
Thus, the rationalized form of the expression \(\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}\) is:

\[ 5 + 2\sqrt{6} \]

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