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Simplify $\frac{3}{x-2}+\frac{2x+3}{x^2+2x+4}+\frac{-\left(6x+12\right)}{x^3-8}$

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Solution

Formulas

Videos

Tutorial - Simplify Expressions Dividing simplify numerator, (3 x 2 + 4)/2

https://www.youtube.com/watch?v=5JklSCAtMrk

Algebra 2 - Simplifying a radical expression by multiplying by conjugate, sqrt(x) / (sqrt(x) + 3)

https://www.youtube.com/watch?v=S1A48ASMoYU

Algebra 2 - Dividing two rational expressions by factoring, ((x + y)/6) / ((x^2 - y^2)/3)

https://www.youtube.com/watch?v=mAn_OHWNj2c

Algebra 2 - Graphing a quadratic using a table f(x) = x^2 - 6x + 8

https://www.youtube.com/watch?v=ybDSZcLexCs

Algebra 2 - Applying the equality of logarithms to solve an equation, log3 (3x + 8) = log3 (x^2 + x)

https://www.youtube.com/watch?v=CFxSx6VfS0g

Example 4: Adding and subtracting polynomials | Algebra I | Khan Academy

https://www.youtube.com/watch?v=DMyhUb1pZT0

Function Plot

Plotting: $\frac{-6+5x^2-x}{\left(x-2\right)\left(x^2+2x+4\right)}$

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0
a
b
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d
f
g
m
n
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v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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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Main Topic: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

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