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\frac{7\left(3-\sqrt{2}\right)}{\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)}+\frac{7}{3-\sqrt{2}}=6
Rationalize the denominator of \frac{7}{3+\sqrt{2}} by multiplying numerator and denominator by 3-\sqrt{2}.
\frac{7\left(3-\sqrt{2}\right)}{3^{2}-\left(\sqrt{2}\right)^{2}}+\frac{7}{3-\sqrt{2}}=6
Consider \left(3+\sqrt{2}\right)\left(3-\sqrt{2}\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{7\left(3-\sqrt{2}\right)}{9-2}+\frac{7}{3-\sqrt{2}}=6
Square 3. Square \sqrt{2}.
\frac{7\left(3-\sqrt{2}\right)}{7}+\frac{7}{3-\sqrt{2}}=6
Subtract 2 from 9 to get 7.
3-\sqrt{2}+\frac{7}{3-\sqrt{2}}=6
Cancel out 7 and 7.
3-\sqrt{2}+\frac{7\left(3+\sqrt{2}\right)}{\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)}=6
Rationalize the denominator of \frac{7}{3-\sqrt{2}} by multiplying numerator and denominator by 3+\sqrt{2}.
3-\sqrt{2}+\frac{7\left(3+\sqrt{2}\right)}{3^{2}-\left(\sqrt{2}\right)^{2}}=6
Consider \left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
3-\sqrt{2}+\frac{7\left(3+\sqrt{2}\right)}{9-2}=6
Square 3. Square \sqrt{2}.
3-\sqrt{2}+\frac{7\left(3+\sqrt{2}\right)}{7}=6
Subtract 2 from 9 to get 7.
3-\sqrt{2}+3+\sqrt{2}=6
Cancel out 7 and 7.
6-\sqrt{2}+\sqrt{2}=6
Add 3 and 3 to get 6.
6=6
Combine -\sqrt{2} and \sqrt{2} to get 0.
\text{true}
Compare 6 and 6.
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