The rationalized form is:
[tex]\frac{(\sqrt{x}-5)(\sqrt{x}+2)}{x - 4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{\sqrt{x}-5}{\sqrt{x}-2}[/tex]
To rationalize a denominator, we multiply the numerator and denominator of a fraction with conjugate of the denominator
The conjugate of denominator is:
[tex]\sqrt{x}+2[/tex]
Multiplying with conjugate
[tex]\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}[/tex]
Hence,
The rationalized form is:
[tex]\frac{(\sqrt{x}-5)(\sqrt{x}+2)}{x - 4}[/tex]
Keywords: Conjugate, rationalization
Learn more about rationalization at:
- brainly.com/question/10941043
- brainly.com/question/10978510
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