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Nataly_w [17]
3 years ago
12

rationalize the denominator and simplify with no fractional or negative exponents. please help!! show work please!​

Mathematics
1 answer:
Delicious77 [7]3 years ago
3 0

The rationalized form is:

\frac{(\sqrt{x}-5)(\sqrt{x}+2)}{x - 4}

Step-by-step explanation:

Given

\frac{\sqrt{x}-5}{\sqrt{x}-2}

To rationalize a denominator, we multiply the numerator and denominator of a fraction with conjugate of the denominator

The conjugate of denominator is:

\sqrt{x}+2

Multiplying with conjugate

\frac{\sqrt{x}-5}{\sqrt{x}-2} * \frac{\sqrt{x}+2}{\sqrt{x}+2}\\=\frac{(\sqrt{x}-5)(\sqrt{x}+2)}{(\sqrt{x})^2 - (2)^2}\\=\frac{(\sqrt{x}-5)(\sqrt{x}+2)}{x - 4}

Hence,

The rationalized form is:

\frac{(\sqrt{x}-5)(\sqrt{x}+2)}{x - 4}

Keywords: Conjugate, rationalization

Learn more about rationalization at:

  • brainly.com/question/10941043
  • brainly.com/question/10978510

#LearnwithBrainly

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