To rationalize the denominator of the fraction [tex]\(\frac{7}{\sqrt{10} - 3}\)[/tex], we need to eliminate the square root in the denominator. We achieve this by multiplying both the numerator and the denominator by the conjugate of the denominator.
The conjugate of [tex]\(\sqrt{10} - 3\)[/tex] is [tex]\(\sqrt{10} + 3\)[/tex]. When we multiply by the conjugate, the result in the denominator will be a difference of squares.
So, let's multiply the fraction by [tex]\(\frac{\sqrt{10} + 3}{\sqrt{10} + 3}\)[/tex]:
[tex]\[
\frac{7}{\sqrt{10} - 3} \times \frac{\sqrt{10} + 3}{\sqrt{10} + 3}
\][/tex]
Now, let's calculate the new denominator:
[tex]\[
(\sqrt{10} - 3)(\sqrt{10} + 3) = \sqrt{10}\times\sqrt{10} + \sqrt{10}\times 3 - 3\times\sqrt{10} - 3\times 3 = 10 - 9 = 1
\][/tex]
So the new denominator is 1, and the fraction simplifies to:
[tex]\[
7 \times (\sqrt{10} + 3)
\][/tex]
Therefore, the correct option for rationalizing the denominator is:
B. [tex]\(\sqrt{10} + 3\)[/tex]
