Express (1 + 4 * 7^0.5)/(5 + 2 * 7^0.5) in the form m + n * 7^0.5

Need to make the bottom of the fraction an integer so we can simplify it. The easiest way to do that is the difference of 2 squares so multiply the whole fraction by (5 - 27^0.5). This gives us (5-56+207^0.5-27^0.5)/-3. Simplify to (-51 + 187^0.5)/-3 which gives 17 - 6*7^0.5 as you can seperate the numerator of the fraction to create 2 seperate fractions with the same denominator.