Answer:
8b) 2x+[tex]\sqrt{3}[/tex]x
8c) [tex]\frac{x-3\sqrt{x} +2 }{x-4}[/tex]
Step-by-step explanation:
8b)
Multiply the top and bottom by 2+[tex]\sqrt{3}[/tex] to rationalize this fraction
[tex]\frac{x}{2-\sqrt{3} } * \frac{2+\sqrt{3} }{2+\sqrt{3} }[/tex]
Simplify the product
[tex]\frac{x(2+\sqrt{3}) }{1}[/tex]
Distribute x through the parenthesis
2x+[tex]\sqrt{3}[/tex]x
8c)
Multiply the top and bottom by [tex]\sqrt{x}-2[/tex] to rationalize this fraction
[tex]\frac{(\sqrt{x}-1)*(\sqrt{x}-2) }{(\sqrt{x}+2)*(\sqrt{x}-2) }[/tex]
Simplify the product
[tex]\frac{x-2\sqrt{x}-\sqrt{x}+2 }{x-4}[/tex]
Collect like terms
[tex]\frac{x-3\sqrt{x} +2 }{x-4}[/tex]
