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Simplify the expression $\frac{\frac{3x-6}{x^2+21x+54}}{\frac{40x^2}{x^2+6x+9}}$

Step-by-step Solution

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Final Answer

$\frac{\left(3x-6\right)\left(x+3\right)}{40x^2\left(x+18\right)}$
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Step-by-step Solution

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We can simplify the quotient of fractions $\frac{\frac{3x-6}{x^2+21x+54}}{\frac{40x^2}{x^2+6x+9}}$ by inverting the second fraction and multiply both fractions

$\frac{\left(3x-6\right)\left(x^2+6x+9\right)}{40\left(x^2+21x+54\right)x^2}$

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$\frac{\left(3x-6\right)\left(x^2+6x+9\right)}{40\left(x^2+21x+54\right)x^2}$

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Learn how to solve simplification of algebraic fractions problems step by step online. Simplify the expression ((3x-6)/(x^2+21x+54))/((40x^2)/(x^2+6x+9)). We can simplify the quotient of fractions \frac{\frac{3x-6}{x^2+21x+54}}{\frac{40x^2}{x^2+6x+9}} by inverting the second fraction and multiply both fractions. The trinomial \left(x^2+6x+9\right) is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial.

Final Answer

$\frac{\left(3x-6\right)\left(x+3\right)}{40x^2\left(x+18\right)}$

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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 ((3x-6)/(x^2+21x))/(40x^2/(x^2+6x)) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Plotting: $\frac{\left(3x-6\right)\left(x+3\right)}{40x^2\left(x+18\right)}$

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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 fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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