Ask question

Ask question

All categories

4 years ago

13

What is the correct order of operations for simplifying the expression (x+3)^2-(x^2+9)/2x^2?

1 answer:

Contact [7]4 years ago

3 0

The expression simplified is $\frac{3}{x}$

Step-by-step explanation:

The expression given in this problem is

$\frac{(x+3)^2-(x^2+9)}{2x^2}$

We proceed in the following way:

- First, we solve the square of the brackets:

$\frac{x^2+6x+9-x^2-9}{2x^2}$

- Now we add/subtract the similar terms:

$\frac{(x^2-x^2)+6x+(9-9)}{2x^2}=\frac{6x}{2x^2}$

- And now we simplify by 2x, and we get:

$\frac{6x}{2x^2}=\frac{3}{x}$

Learn more about simplification:

brainly.com/question/7014769

brainly.com/question/1430645

#LearnwithBrainly

You might be interested in

1 , 3 , 6 , 10 , 15

Bas_tet [7]

First difference,

$\Delta_{1} = a_{2} - a_{1} = 3 - 1 = 2 = 1 + 1$

Second difference,

$\Delta_{2} = a_{3} - a_{2} = 6 - 3 = 3 = 2 + 1$

Third difference,

$\Delta_{3} = a_{4} - a_{3} = 10 - 6 = 4 = 3 + 1$

And so on.

Assuming the pattern holds on, we see that

i-th difference,

$\Delta_{i} = a_{i + 1} - a_{i} = i + 1$

$\implies a_{i + 1} = a_{i} + i + 1$

Then, nth term is,

$\implies a_{n} = a_{n - 1} + n$

$= a_{n - 2}+ (n + (n - 1))$

$= a_{n - 3} + (n + (n - 1) +(n - 2))$

$= a_{n - (n - 1)} + \sum \limits^{n - 2}_{k = 0}(n - k)$

$= a_1 + \sum \limits^{n - 2}_{k = 0}n- \sum \limits^{n - 2}_{k = 0}k$

$= a_1 +n(n -2 + 1 )- \frac{1}{2} (n - 2)(n - 1)$

$= a_1 +n(n -1 )- \frac{1}{2} (n - 2)(n - 1)$

$= a_1 +(n -1 )(n- \frac{1}{2} (n - 2))$

$= a_1 + \frac{1}{2} (n -1 )(2n- n + 2)$

$= a_1 + \frac{1}{2} (n -1 )(n + 2)$

$\implies a_{n} = 1 + \frac{1}{2} (n -1 )(n + 2)$

Now, the 21st term in the sequence is,

$\implies a_{21} = 1 + \frac{1}{2} (21 -1 )(21 + 2)$

$= 1 + \frac{1}{2} \times 20 \times 23$

$= 231$

4 0

3 years ago

The sum of 5 times a number and 3 is 4

mrs_skeptik [129]

Answer:

5x+3=4

Step-by-step explanation:

I hope this helps.

8 0

3 years ago

Read 2 more answers

A cylindrical pressure vessel has a height of 9 feet and a diameter of 6 feet. How much gas can the pressure vessel hold when fu

notka56 [123]

since the diameter of the base of the cylinder is 6 feet, then its radius is half that, or 3 feet.

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h~~
\begin{cases}
r=radius\\
h=height\\[-0.5em]
\hrulefill\\
r=3\\
h=9
\end{cases}\implies V=\pi (3)^2(9)\implies V=81\pi$

5 0

3 years ago

Read 2 more answers

Describe a free market economy

antoniya [11.8K]

DescriptionA market economy is an economic system in which the decisions regarding investment, production and distribution are guided by the price signals created by the forces of supply and demand.

6 0

3 years ago

Read 2 more answers

In the diagram below, OP is circumscribed about quadrilateral ABCD. What is

elena-s [515]

Answer:

The value of X=180-98

=82

6 0

3 years ago