Evaluate
\sqrt{10}-\sqrt{7}\approx 0.516526349
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\frac{3\left(\sqrt{7}-\sqrt{10}\right)}{\left(\sqrt{7}+\sqrt{10}\right)\left(\sqrt{7}-\sqrt{10}\right)}
Rationalize the denominator of \frac{3}{\sqrt{7}+\sqrt{10}} by multiplying numerator and denominator by \sqrt{7}-\sqrt{10}.
\frac{3\left(\sqrt{7}-\sqrt{10}\right)}{\left(\sqrt{7}\right)^{2}-\left(\sqrt{10}\right)^{2}}
Consider \left(\sqrt{7}+\sqrt{10}\right)\left(\sqrt{7}-\sqrt{10}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{3\left(\sqrt{7}-\sqrt{10}\right)}{7-10}
Square \sqrt{7}. Square \sqrt{10}.
\frac{3\left(\sqrt{7}-\sqrt{10}\right)}{-3}
Subtract 10 from 7 to get -3.
-\left(\sqrt{7}-\sqrt{10}\right)
Cancel out -3 and -3.
-\sqrt{7}-\left(-\sqrt{10}\right)
To find the opposite of \sqrt{7}-\sqrt{10}, find the opposite of each term.
-\sqrt{7}+\sqrt{10}
The opposite of -\sqrt{10} is \sqrt{10}.
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