Answer:
[tex] a = \dfrac{5}{18} [/tex]
[tex]b = -\dfrac{1}{18}[/tex]
Step-by-step explanation:
You need to rationalize the fraction.
[tex] \dfrac{1}{5 + \sqrt{7}} = a + b\sqrt{7} [/tex]
[tex] \dfrac{1}{5 + \sqrt{7}} \times \dfrac{5 - \sqrt{7}}{5 - \sqrt{7}} = a + b\sqrt{7} [/tex]
[tex] \dfrac{5 - \sqrt{7}}{25 - 7} = a + b\sqrt{7} [/tex]
[tex] \dfrac{5 - \sqrt{7}}{18} = a + b\sqrt{7} [/tex]
[tex] \dfrac{5}{18} - \dfrac{1}{18}\sqrt{7} = a + b\sqrt{7} [/tex]
[tex] a = \dfrac{5}{18} [/tex]
[tex]b = -\dfrac{1}{18}[/tex]
