SOLUTION: Can you simplify by rationalizing the denominator ? Help (12)/(6-√13) 12 over 6 minus √13 Thank you so much

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Question 1040262: Can you simplify by rationalizing the denominator ?
Help
(12)/(6-√13)
12 over 6 minus √13
Thank you so much
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
(12)/(6-√13) 
12 over 6 minus √13

12%2F%286-sqrt%2813%29%29

Form the conjugate of the two term denominator
by the rule: A+B and A-B are conjugates of each
other.

So the conjugate of 6-sqrt%2813%29 is 6%2Bsqrt%2813%29.

Then put the conjugate over itself, %286%2Bsqrt%2813%29%29%2F%286%2Bsqrt%2813%29%29,
which equals 1, and since it equals 1, we can multiply
12%2F%286-sqrt%2813%29%29 by it without changing its value.

12%2F%286-sqrt%2813%29%29%22%22%2A%22%22%286%2Bsqrt%2813%29%29%2F%286%2Bsqrt%2813%29%29

%2812%2A%286-sqrt%2813%29%29%29%2F%28%286-sqrt%2813%29%29%286%2Bsqrt%2813%29%29%29

FOIL out the bottom:

%2812%2A%286-sqrt%2813%29%29%29%2F%2836%2B6sqrt%2813%29-6sqrt%2813%29-13%29



%2812%2A%286-sqrt%2813%29%29%29%2F%2836-13%29

%2812%2A%286%2Bsqrt%2813%29%29%29%2F23

expr%2812%2F23%29%2A%286%2Bsqrt%2813%29%29%29

Either of the last two forms.

Edwin

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
For more solved problems on rationalizing the denominator see the lesson

      HOW TO rationalize a fraction by making its denominator free of square roots

in this site.