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timurjin [86]
3 years ago
13

Simplify the expression given below. x+2/4x^2+5x+1 * 4x+1/x^2-4

Mathematics
1 answer:
GenaCL600 [577]3 years ago
8 0

Answer:

\frac{1}{(x+1)(x-2)}

Step-by-step explanation:

\frac{x+2}{4x^2 + 5x + 1} \ \times \ \frac{4x+1}{x^2-4}\\\\=\frac{x+2}{4x^2 + 4x  + x + 1} \ \times \ \frac{4x+1}{x^2-2^2}\\\\=\frac{x+2}{4x(x + 1)  + 1( x + 1)} \ \times \ \frac{4x+1}{(x - 2)(x + 2)}    \ \ \ \ \  \ \ \ [ \ (a^2 - b^2 = (a-b)(a+b) \ ]\\\\\\=\frac{x+2}{(4x + 1)(x+1)} \ \times \ \frac{4x+1}{(x-2)(x+2)}\\\\=\frac{1}{(x+1)} \ \times \ \frac{1}{(x-2)}\\\\= \frac{1}{(x+1)(x-2)}

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A bottle contains 20 blue bags and 15 red bags. If two bags are picked at random one after the other with replacement, what is t
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Answer:

<h2> 12÷49</h2>

Step-by-step explanation:

The total number of bags in the bottle = 20 + 15 = 35

Then

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the probability that the second (picked) bag is blue = 15/35

Conclusion:

If two bags are picked at random one after the other with replacement

Then

the probability that the first bag is blue and then red is :

(20÷35)×(15÷35)

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Answer:

Given that

                                                                 1

John can run 100 meters dash in 16    --------- seconds .

                                                                  5

Savanna 's time is 19.8 seconds .

Here we have John time in mixed fraction and Savanna's time in decimal .

Converting mixed fraction into improper .

     1                      16 * 5     +  1                 80 + 1                 81

16  --------    =     ---------------------------    =   -------------- =   - -----------

    5                           5                                  5                      5

Thus we got John time as 81 /5 seconds .

Converting Savanna's time in fraction , we get

 19 8

----------  seconds .

  10  

We have two fractions with different denominator .

One is having denominator 5 and another is having denominator 10 .

We need to make the denominator same of both the fraction .

We need to make denominator 10 .

Multiply John fraction by 2 in both numerator and denominator by 2 to make denominator 10 .

81 * 2               162

----------  =      ------------ seconds .

5 *  2                   10

John is taking less time than Savanna . Thus John is faster .

Difference

198          162            36

-------  -     -------     =  ------- seconds  

10              10              10

Thus John is faster by  (36/10 ) seconds  =  3.6 seconds.

Step-by-step explanation:

Given that

                                                                 1

John can run 100 meters dash in 16    --------- seconds .

                                                                  5

Savanna 's time is 19.8 seconds .

Here we have John time in mixed fraction and Savanna's time in decimal .

Converting mixed fraction into improper .

     1                      16 * 5     +  1                 80 + 1                 81

16  --------    =     ---------------------------    =   -------------- =   - -----------

    5                           5                                  5                      5

Thus we got John time as 81 /5 seconds .

Converting Savanna's time in fraction , we get

 19 8

----------  seconds .

  10  

We have two fractions with different denominator .

One is having denominator 5 and another is having denominator 10 .

We need to make the denominator same of both the fraction .

We need to make denominator 10 .

Multiply John fraction by 2 in both numerator and denominator by 2 to make denominator 10 .

81 * 2               162

----------  =      ------------ seconds .

5 *  2                   10

John is taking less time than Savanna . Thus John is faster .

Difference

198          162            36

-------  -     -------     =  ------- seconds  

10              10              10

Thus John is faster by  (36/10 ) seconds  =  3.6 seconds.

4 0
2 years ago
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