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omeli [17]
3 years ago
9

Simplify the expression state any excluded values 2a^2-4a+2 --------------- 3a^2-3

Mathematics
1 answer:
chubhunter [2.5K]3 years ago
8 0

Answer:

The simplified form is \dfrac{2(x-1)}{3(x+1)}.

x =1 is the excluded value for the given expression.

Step-by-step explanation:

Given:

The expression given is:

\dfrac{2a^2-4a+2}{3a^2-3}

Let us simplify the numerator and denominator separately.

The numerator is given as 2a^2-4a+2

2 is a common factor in all the three terms. So, we factor it out. This gives,

=2(a^2-2a+1)

Now, a^2-2a+1=(a-1)(a-1)

Therefore, the numerator becomes 2(a-1)(a-1)

The denominator is given as: 3a^2-3

Factoring out 3, we get

3(a^2-1)

Now, a^2-1 is of the form a^2-b^2=(a-b)(a+b)

So, a^2-1=(a-1)(a+1)

Therefore, the denominator becomes 3(a-1)(a+1)

Now, the given expression is simplified to:

\frac{2a^2-4a+2}{3a^2-3}=\frac{2(x-1)(x-1)}{3(x-1)(x+1)}

There is (x-1) in the numerator and denominator. We can cancel them only if x\ne1 as for x=1, the given expression is undefined.

Now, cancelling the like terms considering x\ne1, we get:

\dfrac{2a^2-4a+2}{3a^2-3}=\dfrac{2(x-1)}{3(x+1)}

Therefore, the simplified form is \dfrac{2(x-1)}{3(x+1)}

The simplification is true only if  x\ne1. So, x =1 is the excluded value for the given expression.

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Answer:

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2 years ago
A building casts a shawdow 48 feet long. At the same time, A 40 feet tall flag pole casts a shadow 9.6 feet long. What is the he
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3 years ago
A bag had 7 orange rocks , 6 green rock , 1 white rock ,7 black rocks , and 2 yellow you randomly pull a rock from the bag ,keep
daser333 [38]

Answer:

Probability = \frac{7}{253}

Step-by-step explanation:

Given

Orange = 7

Green = 6

White = 1

Black = 7

Yellow = 2

Required

Probability of selecting a yellow then orange rock

From the question, we understand that the probability is that of without replacement.

Since the yellow, is first picked.

We need to determine the probability of picking a yellow rock, first.

P(Yellow) = \frac{n(Yellow)}{Total}

P(Yellow) = \frac{2}{7 + 6 + 1 + 7 + 2}

P(Yellow) = \frac{2}{23}

The rock has reduced by 1;

Next is to determine the probability of picking an orange rock

P(Orange) = \frac{n(Orange)}{Total - 1}

P(Orange) = \frac{7}{7 + 6 + 1 + 7 + 2- 1}

P(Orange) = \frac{7}{22}

The required probability is calculated as thus:

Probability = P(Yellow) * P(Orange)

Probability = \frac{2}{23} * \frac{7}{22}

Probability = \frac{14}{506}

Probability = \frac{7}{253}

4 0
3 years ago
Gerald bought 3 shirts for 8.40 each, 2 shirts for 12.89 each, and one shirt for 18.90. What was the average cost of the shirts?
Vanyuwa [196]
So first, you add all the numbers together

8.40*3=25.20
12.89*2=25.78
18.90*1=18.90
____________
$69.88

Divide the number of shirts: 6 by the total amount


69.88
_____ = $11.64666= $11.65 is your answer!
6
8 0
3 years ago
Read 2 more answers
the graph of a liner relationship has a slope of -5 and passes through the point (2, -12). write tge equation of the liner in th
bixtya [17]

Answer:

y = -5x - 2

Step-by-step explanation:

equation formula: y = mx + c

m = -5

-12 = -5(2) + c

c = -2

⇒ y = -5x - 2

5 0
2 years ago
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