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Simplify the expression $\frac{3}{\frac{2x^3-5x^2-2x-3}{4x^3-13x^2+4x-3}}$

Step-by-step Solution

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Final Answer

$\frac{3\left(4x^{2}-x+1\right)}{2x^{2}+x+1}$
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Step-by-step Solution

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Divide fractions $\frac{3}{\frac{2x^3-5x^2-2x-3}{4x^3-13x^2+4x-3}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$

$\frac{3\left(4x^3-13x^2+4x-3\right)}{2x^3-5x^2-2x-3}$

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$\frac{3\left(4x^3-13x^2+4x-3\right)}{2x^3-5x^2-2x-3}$

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Learn how to solve simplification of algebraic expressions problems step by step online. Simplify the expression 3/((2x^3-5x^2-2x+-3)/(4x^3-13x^24x+-3)). Divide fractions \frac{3}{\frac{2x^3-5x^2-2x-3}{4x^3-13x^2+4x-3}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. We can factor the polynomial \left(4x^3-13x^2+4x-3\right) using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -3. Next, list all divisors of the leading coefficient a_n, which equals 4. The possible roots \pm\frac{p}{q} of the polynomial \left(4x^3-13x^2+4x-3\right) will then be.

Final Answer

$\frac{3\left(4x^{2}-x+1\right)}{2x^{2}+x+1}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind 3/((2x^3+-5x^2)/(4x^3+-13x^2)) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Plotting: $\frac{3\left(4x^{2}-x+1\right)}{2x^{2}+x+1}$

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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

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Main Topic: Simplification of algebraic expressions

The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.

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