Question

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

Answer 1

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

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