Solve the rational equation $y=\sqrt[5]{\frac{\left(x+4\right)\left(x^2-1\right)^3}{x^2+x+2}}$

Step-by-step Solution

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Final answer to the problem

$y=\sqrt[5]{\frac{\left(x+4\right)\left(x^2-1\right)^3}{\left(x+\frac{1}{2}\right)^2+\frac{7}{4}}}$
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Step-by-step Solution

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  • Find the derivative
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1

Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

Learn how to solve completing the square problems step by step online.

$y=\sqrt[5]{\frac{\left(x+4\right)\left(x^2-1\right)^3}{x^2+x+2+\frac{1}{4}-\frac{1}{4}}}$

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Unlock the first 3 steps of this solution

Learn how to solve completing the square problems step by step online. Solve the rational equation y=(((x+4)(x^2-1)^3)/(x^2+x+2))^(1/5). Add and subtract \displaystyle\left(\frac{b}{2a}\right)^2. Factor the perfect square trinomial x^2+x+\frac{1}{4}. Calculate the power \sqrt{\frac{1}{4}}. Simplify the addition \left(x+\frac{1}{2}\right)^2+2-\frac{1}{4}.

Final answer to the problem

$y=\sqrt[5]{\frac{\left(x+4\right)\left(x^2-1\right)^3}{\left(x+\frac{1}{2}\right)^2+\frac{7}{4}}}$

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Function Plot

Plotting: $y-\sqrt[5]{\frac{\left(x+4\right)\left(x^2-1\right)^3}{x^2+x+2}}$

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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

How to improve your answer:

Main Topic: Completing the Square

In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form ax^2+bx+c to the form a(x+h)^2+k.

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