Answer:
[tex]\frac{3(\sqrt{3} -\sqrt{x})}{3-x}[/tex] or [tex]\frac{3\sqrt{3}-3\sqrt{x} }{3-x}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{9} }{\sqrt{3} +\sqrt{x} }[/tex]
[tex]\frac{3}{\sqrt{3}+\sqrt{x} }[/tex]
Multiply by the opposite by using the difference of squares converse formula.
[tex]\frac{3}{\sqrt{3} +\sqrt{x} } *\frac{\sqrt{3} -\sqrt{x}}{\sqrt{3} -\sqrt{x}}[/tex]
[tex]\frac{3(\sqrt{3} -\sqrt{x})}{3-x}[/tex]
[tex]\frac{3\sqrt{3}-3\sqrt{x} }{3-x}[/tex]
Answer:
3 sqrt(3) - 3 sqrt(x)
---------------------------
3 - x
Step-by-step explanation:
sqrt(9) = 3
so writing the expression as
3
--------------------
sqrt(3) + sqrt(x)
Multiply by the conjugate, sqrt(3) - sqrt(x) in the numerator and denominator
3 sqrt(3) - sqrt(x)
-------------------- * ------------------
sqrt(3) + sqrt(x) sqrt(3) - sqrt(x)
Foil the denominator
3 sqrt(3) - 3 sqrt(x)
---------------------------
sqrt(3) sqrt(3) + sqrt(3x) - sqrt(3x) - sqrt(x^2)
Simplify
3 sqrt(3) - 3 sqrt(x)
---------------------------
3 - x
