Answer:
[tex] \large \boxed{\bold{2}}[/tex]
Step-by-step explanation:
[tex]\frac{4}{3 + \sqrt{7}} \\ [/tex]
Rationalise the denominator by multiplying the numerator & denominator of the fraction with [tex](3 - \sqrt{7})[/tex].
[tex]\frac{4\left(3-\sqrt{7}\right)}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)} \\ [/tex]
Now, we an see that the denominator is in the form of the algebraic identity: (x + y) (x - y) = x² - y². So,
[tex]\frac{4\left(3-\sqrt{7}\right)}{3^{2}-\left(\sqrt{7}\right)^{2}} \\= \frac{4\left(3-\sqrt{7}\right)}{9-7} \\= \frac{4\left(3-\sqrt{7}\right)}{2} \\[/tex]
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