How would I write (1+4(root)7)/(5+2(root)7) in the form m + n(root)7, where m and n are integers?

We know that any value divided by itself is equal to 1, therefore we can multiply the value in the question by (5-2(root)7)/(5-2(root)7) and the value would not change. We are only changing the values format. We do this because we want to get the denominator to an integer value so we can divide the numerator easily, we know that (root)7 multiplied by (root)7 will give us 7.Thus eventually we will get the answer 17-6(root)7 where m=17 and n=6.
Can demonstrate this on whiteboard if needs be.