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[tex]\frac{3/7}{7\sqrt{10}/2 }[/tex]How do I simplify this problem? I have radical in the denominator and a fraction in the numerator.

Sagot :

LammettHash

Multiply the numerator and denominator by 7×2 = 14 to eliminate the denominators of those fractions:

[tex]\dfrac{\dfrac37}{\dfrac{7\sqrt{10}}2}\times\dfrac{14}{14}=\dfrac{3\times2}{7\sqrt{10}\times7}=\dfrac6{49\sqrt{10}}[/tex]

Rationalize the denominator by multiplying both numerator and denominator by √10:

[tex]\dfrac6{49\sqrt{10}}\times\dfrac{\sqrt{10}}{\sqrt{10}}=\dfrac{6\sqrt{10}}{49(\sqrt{10})^2}=\dfrac{6\sqrt{10}}{49\times10}=\dfrac{6\sqrt{10}}{490}[/tex]

Lastly, cancel the common factor of 2 in both the numerator and denominator (which comes from 6 = 2×3 and 490 = 2×245):

[tex]\dfrac{6\sqrt{10}}{490}=\dfrac{3\sqrt{10}}{245}}[/tex]

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