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Llana [10]
3 years ago
9

The fraction a/b is in simplest terms and equal to the following:((2020^3)-1)/((2021^3)+1) . What is a + b?

Mathematics
1 answer:
blagie [28]3 years ago
7 0

Consider the expression

\dfrac{x^3-1}{(x+1)^3+1}

Factorize the numerator and denominator a difference/sum of cubes:

\dfrac{(x-1)(x^2+x+1)}{((x+1)+1)((x+1)^2-(x+1)+1)}

Expand the denominator:

\dfrac{(x-1)(x^2+x+1)}{(x+2)((x^2+2x+1)-(x+1)+1)}=\dfrac{(x-1)(x^2+x+1)}{(x+2)(x^2+x+1)}=\dfrac{x-1}{x+2}

since <em>x</em> = 2020, and clearly 2020² + 2020 + 1 ≠ 0, so we can cancel the factor of <em>x</em> ² + <em>x</em> + 1. This leaves us with

\dfrac{2020^3-1}{2021^3+1} = \dfrac{2020-1}{2020+2} = \dfrac{2019}{2022}=\dfrac{673}{674}=\dfrac ab

so that <em>a</em> + <em>b</em> = 673 + 674 = 1347.

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∘

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17

3

)

=

17

Therefore,

(

h

∘

f

∘

g

)

(

1

)

=

17

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(

h

∘

f

∘

g

)

(

x

)

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x

in  

f

(

x

)

with the function  

g

(

x

)

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in  

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(

x

)

with the function of  

(

f

∘

g

)

(

x

)

, to get  

(

h

∘

f

∘

g

)

(

x

)

.

This, simplified, is equal to  

2

x

+

15

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h

∘

f

∘

g

)

(

1

)

=

2

(

1

)

+

15

=

17

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5 0
3 years ago
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Rudiy27

Answer:

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3 0
2 years ago
A pharmaceutical company sells bottles of 500 calcium tablets in two dosages: 250 milligram and 500 milligram. Last month, the c
Svetach [21]
X = 250 mg tabs
y = 500 mg tabs

2200x + 1800y = 39200....multiply by -1
2200x + 2200y = 44000
--------------------------------
-2200x - 1800y = - 39200 (result of multiplying by -1)
2200x + 2200y = 44000
--------------------------------add
400y = 4800
y = 4800/400
y = 12...... the 500 mg tabs (y) costs $ 12 per bottle

2200x + 2200y = 44000
2200x + 2200(12) = 44000
2200x + 26400 = 44000
2200x = 44000 - 26400
2200x = 17600
x = 17600/2200
x = 8 <== the 250 mg tabs (x) costs $ 8 per bottle
3 0
3 years ago
Read 2 more answers
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