Sure, let's simplify the expression [tex]\(\frac{\sqrt{3636.09} + \sqrt{2862.25}}{\sqrt{3636.09} - \sqrt{2862.25}}\)[/tex].
1. First, we need to find the square roots of the numbers inside the radicals.
[tex]\[
\sqrt{3636.09} = 60.3
\][/tex]
[tex]\[
\sqrt{2862.25} = 53.5
\][/tex]
2. Next, substitute these values back into the original expression:
[tex]\[
\frac{60.3 + 53.5}{60.3 - 53.5}
\][/tex]
3. Now, we evaluate the numerator and the denominator separately:
Numerator:
[tex]\[
60.3 + 53.5 = 113.8
\][/tex]
Denominator:
[tex]\[
60.3 - 53.5 = 6.8
\][/tex]
4. Finally, divide the numerator by the denominator:
[tex]\[
\frac{113.8}{6.8} = 16.73529411764705
\][/tex]
So, the simplified result of the given expression is approximately [tex]\(16.735\)[/tex].
