[tex] \frac{7}{5 \sqrt{2} - 1} = \frac{7(5 \sqrt{2} + 1)}{(5 \sqrt{2} - 1)(5 \sqrt{2} + 1)} [/tex]
[tex] = \frac{35 \sqrt{2} + 7 }{( {5 \sqrt{2} )}^{2} - {1}^{2} } [/tex]
[tex] = \frac{35 \sqrt{2} + 7}{50 - 1} [/tex]
[tex] = \frac{35 \sqrt{2} + 7}{49} [/tex]
[tex] = \frac{7(5 \sqrt{2} + 1)}{49} [/tex]
[tex] = \frac{5 \sqrt{2} + 1}{7} [/tex]
[tex] = \frac{5 \times 1.41 + 1}{7} [/tex]
[tex] = \frac{7.05 + 1}{7} [/tex]
[tex] = \frac{8.05}{7} [/tex]
[tex] = 1.15[/tex]
[tex][1.15 ] = 1[/tex]
[tex] {1.15} = 1.15 - [1.15 ] [/tex]
[tex] = 1.15 - 1[/tex]
[tex] = 0.15[/tex]
