Rationalize and simplify the expression $\frac{2}{3+\sqrt{3}}$

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Final answer to the problem

$\frac{2\left(3-\sqrt{3}\right)}{6}$
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Step-by-step Solution

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Apply the formula: $\frac{a}{b}$$=\frac{a}{b}\frac{conjugate\left(b\right)}{conjugate\left(b\right)}$, where $a=2$, $b=3+\sqrt{3}$ and $a/b=\frac{2}{3+\sqrt{3}}$

$\frac{2}{3+\sqrt{3}}\cdot \frac{3-\sqrt{3}}{3-\sqrt{3}}$

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$\frac{2}{3+\sqrt{3}}\cdot \frac{3-\sqrt{3}}{3-\sqrt{3}}$

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Learn how to solve rationalisation problems step by step online. Rationalize and simplify the expression 2/(3+3^(1/2)). Apply the formula: \frac{a}{b}=\frac{a}{b}\frac{conjugate\left(b\right)}{conjugate\left(b\right)}, where a=2, b=3+\sqrt{3} and a/b=\frac{2}{3+\sqrt{3}}. Apply the formula: \frac{a}{b}\frac{c}{f}=\frac{ac}{bf}, where a=2, b=3+\sqrt{3}, c=3-\sqrt{3}, a/b=\frac{2}{3+\sqrt{3}}, f=3-\sqrt{3}, c/f=\frac{3-\sqrt{3}}{3-\sqrt{3}} and a/bc/f=\frac{2}{3+\sqrt{3}}\cdot \frac{3-\sqrt{3}}{3-\sqrt{3}}. Apply the formula: \left(a+b\right)\left(a+c\right)=a^2-b^2, where a=3, b=\sqrt{3}, c=-\sqrt{3}, a+c=3-\sqrt{3} and a+b=3+\sqrt{3}. Apply the formula: a+b=a+b, where a=9, b=-3 and a+b=9-3.

Final answer to the problem

$\frac{2\left(3-\sqrt{3}\right)}{6}$

Exact Numeric Answer

$0.42265$

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Plotting: $\frac{2\left(3-\sqrt{3}\right)}{6}$

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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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