Rationalize and simplify the expression $\frac{3}{5+\sqrt{3}}$

Step-by-step Solution

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Final answer to the problem

$\frac{3\left(5-\sqrt{3}\right)}{22}$
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Step-by-step Solution

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1

Multiply and divide the fraction $\frac{3}{5+\sqrt{3}}$ by the conjugate of it's denominator $5+\sqrt{3}$

Learn how to solve factor by difference of squares problems step by step online.

$\frac{3}{5+\sqrt{3}}\cdot \frac{5-\sqrt{3}}{5-\sqrt{3}}$

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Learn how to solve factor by difference of squares problems step by step online. Rationalize and simplify the expression 3/(5+3^(1/2)). Multiply and divide the fraction \frac{3}{5+\sqrt{3}} by the conjugate of it's denominator 5+\sqrt{3}. Multiplying fractions \frac{3}{5+\sqrt{3}} \times \frac{5-\sqrt{3}}{5-\sqrt{3}}. Solve the product of difference of squares \left(5+\sqrt{3}\right)\left(5-\sqrt{3}\right). Add the values 25 and -3.

Final answer to the problem

$\frac{3\left(5-\sqrt{3}\right)}{22}$

Exact Numeric Answer

$0.445629$

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Function Plot

Plotting: $\frac{3\left(5-\sqrt{3}\right)}{22}$

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7
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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

How to improve your answer:

Main Topic: Factor by Difference of Squares

The difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2=(a+b)(a-b) in elementary algebra.

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