Rationalize and simplify the expression $\frac{3}{\sqrt{7}-2}$

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Final answer to the problem

$\sqrt{7}+2$
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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 $a=3$, $b=\sqrt{7}-2$ and $a/b=\frac{3}{\sqrt{7}-2}$

$\frac{3}{\sqrt{7}-2}\cdot \frac{\sqrt{7}+2}{\sqrt{7}+2}$

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$\frac{3}{\sqrt{7}-2}\cdot \frac{\sqrt{7}+2}{\sqrt{7}+2}$

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Learn how to solve rationalisation problems step by step online. Rationalize and simplify the expression 3/(7^(1/2)-2). Apply the formula: \frac{a}{b}=\frac{a}{b}\frac{conjugate\left(b\right)}{conjugate\left(b\right)}, where a=3, b=\sqrt{7}-2 and a/b=\frac{3}{\sqrt{7}-2}. Apply the formula: \frac{a}{b}\frac{c}{f}=\frac{ac}{bf}, where a=3, b=\sqrt{7}-2, c=\sqrt{7}+2, a/b=\frac{3}{\sqrt{7}-2}, f=\sqrt{7}+2, c/f=\frac{\sqrt{7}+2}{\sqrt{7}+2} and a/bc/f=\frac{3}{\sqrt{7}-2}\cdot \frac{\sqrt{7}+2}{\sqrt{7}+2}. Apply the formula: \left(a+b\right)\left(a+c\right)=a^2-b^2, where a=\sqrt{7}, b=2, c=-2, a+c=\sqrt{7}+2 and a+b=\sqrt{7}-2. Apply the formula: a+b=a+b, where a=7, b=-4 and a+b=7-4.

Final answer to the problem

$\sqrt{7}+2$

Exact Numeric Answer

$4.645751$

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Function Plot

Plotting: $\sqrt{7}+2$

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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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