Rationalize and simplify the expression $\frac{x^2}{\sqrt{x^2+4x+2^2}-2}$

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Final answer to the problem

$\frac{x^2\left(\sqrt{x^2+4x+2^2}+2\right)}{x^2+4x}$
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Multiply and divide the fraction $\frac{x^2}{\sqrt{x^2+4x+2^2}-2}$ by the conjugate of it's denominator $\sqrt{x^2+4x+2^2}-2$

$\frac{x^2}{\sqrt{x^2+4x+2^2}-2}\frac{\sqrt{x^2+4x+2^2}+2}{\sqrt{x^2+4x+2^2}+2}$

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$\frac{x^2}{\sqrt{x^2+4x+2^2}-2}\frac{\sqrt{x^2+4x+2^2}+2}{\sqrt{x^2+4x+2^2}+2}$

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Learn how to solve rationalisation problems step by step online. Rationalize and simplify the expression (x^2)/((x^2+4x2^2)^(1/2)-2). Multiply and divide the fraction \frac{x^2}{\sqrt{x^2+4x+2^2}-2} by the conjugate of it's denominator \sqrt{x^2+4x+2^2}-2. Multiplying fractions \frac{x^2}{\sqrt{x^2+4x+2^2}-2} \times \frac{\sqrt{x^2+4x+2^2}+2}{\sqrt{x^2+4x+2^2}+2}. Solve the product of difference of squares \left(\sqrt{x^2+4x+2^2}-2\right)\left(\sqrt{x^2+4x+2^2}+2\right). Add the values 4 and -4.

Final answer to the problem

$\frac{x^2\left(\sqrt{x^2+4x+2^2}+2\right)}{x^2+4x}$

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Plotting: $\frac{x^2\left(\sqrt{x^2+4x+2^2}+2\right)}{x^2+4x}$

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5
6
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

How to improve your answer:

Main Topic: Rationalisation

In elementary algebra, root rationalisation is a process by which radicals in the denominator of an algebraic fraction are eliminated.

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