SOLUTION: 1 minus square root of 7 on the numerator divided by 3 plus square root of 7 on the demoninator. Can you please go through the steps to rationalize the denominator in the problem.

Algebra ->  Radicals -> SOLUTION: 1 minus square root of 7 on the numerator divided by 3 plus square root of 7 on the demoninator. Can you please go through the steps to rationalize the denominator in the problem.      Log On


   

Question 153907: 1 minus square root of 7 on the numerator divided by 3 plus square root of 7 on the demoninator. Can you please go through the steps to rationalize the denominator in the problem. Thank-you very much!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
+%281-sqrt%287%29%29%2F%283%2Bsqrt%287%29%29+
.
The strategy is to get rid of all square root symbols in the denominator. Do this by first multiplying by: +%283-sqrt%287%29%29%2F%283-sqrt%287%29%29+
.
So, we have:
+%281-sqrt%287%29%29%2F%283%2Bsqrt%287%29%29+%2A+%283-sqrt%287%29%29%2F%283-sqrt%287%29%29+
.
Performing "FOIL" on the denominator:
+%28%281-sqrt%287%29%29%2A%283-sqrt%287%29%29%29%2F%289-3sqrt%287%29%2B3sqrt%287%29-7%29+
Reducing the denominator:
+%28%281-sqrt%287%29%29%2A%283-sqrt%287%29%29%29%2F%289-7%29+
+%28%281-sqrt%287%29%29%2A%283-sqrt%287%29%29%29%2F%282%29+
.
Performing "FOIL" on the numerator:
+%283-sqrt%287%29-3sqrt%287%29%2B7%29%2F%282%29+
Reducing the numerator:
+%2810-4sqrt%287%29%29%2F%282%29+
.
Finally, we can reduce it to (by dividing each term in the numerator by 2):
+5-2sqrt%287%29+