Solve the rational equation $y=\frac{\sqrt[3]{x^3-8}\sqrt{x^2+1}}{2x^6+7x-4}$

Step-by-step Solution

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Final answer to the problem

$y=\frac{\sqrt[3]{x+2}\sqrt[3]{x^{2}-2x+4}\sqrt{x^2+1}}{2x^6+7x-4}$
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Step-by-step Solution

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1

Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$

Learn how to solve factorization problems step by step online.

$y=\frac{\sqrt[3]{\left(\sqrt[3]{x^3}+\sqrt[3]{8}\right)\left(\sqrt[3]{\left(x^3\right)^{2}}-\sqrt[3]{8}\sqrt[3]{x^3}+\sqrt[3]{\left(8\right)^{2}}\right)}\sqrt{x^2+1}}{2x^6+7x-4}$

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Learn how to solve factorization problems step by step online. Solve the rational equation y=((x^3-8)^(1/3)(x^2+1)^(1/2))/(2x^6+7x+-4). Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Calculate the power \sqrt[3]{8}. Calculate the power \sqrt[3]{8}. Multiply -1 times 2.

Final answer to the problem

$y=\frac{\sqrt[3]{x+2}\sqrt[3]{x^{2}-2x+4}\sqrt{x^2+1}}{2x^6+7x-4}$

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Function Plot

Plotting: $y+\frac{-\sqrt[3]{x^3-8}\sqrt{x^2+1}}{2x^6+7x-4}$

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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: Factorization

In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.

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