You can identify terms and count them before you start factoring. Doing so will identify 3x² as a term in the numerator, and will show you there are 3 terms in the denominator.

When you factor the expression, you get ...

$\dfrac{3x^2-3}{3x^2+2x-1}=\dfrac{3(x^2-1)}{(3x-1)(x+1)}=\dfrac{3(x-1)(x+1)}{(3x-1)(x+1)}$

This reveals a common factor of x+1.

So, the above three observations are true of this rational expression.

3 0

3 years ago

**view image**

vladimir1956 [14]

The chart has been completed in the picture attached.

Step-by-step explanation:

Step 1:

It is given that the number of bacteria doubles every 6 hours.

So if there are 1 million now, in 6 hours there would be double that i.e. 2 million and it will go on.

Step 2:

As the first column says the number of 6-hour periods, the second column is the actual number of hours.

So the second column is multiples of 6 so the second column is filled with;

0, 6, 12, 18, 24, 30, 36, 42 and 48.

Step 3:

The current population is calculated by multiplying the previous population by 2.

For 0 hours, the population = 3 million,

For 6 hours, the population = $2(3) = 6$ million,

For 12 hours, the population = $2(6) = 12$ million,

For 18 hours, the population = $2(12) = 24$ million,

For 24 hours, the population = $2(24) = 48$ million,

For 30 hours, the population = $2(48) = 96$ million,

For 36 hours, the population = $2(96) = 192$ million,

For 42 hours, the population = $2(192) = 384$ million, and

For 48 hours, the population = $2(384) = 768$ million.

So at the end of 48 hours, there will be approximately 768 million bacteria on the pinhead.

8 0

2 years ago