Question

Write an algebraic expression that describes this set of calculations.
step 1- take some number and square it.
step 2- add 2 times the starting number
step 3- divide that result by your starting number.
step 4- subtract your starting number.

Answer 1

What the equation for step 1?

Answer 2

call the number x

Answer 3

i dont know. it just says that we need to take any number.

Answer 4

Yes, so call that arbitrary starting number x. The first step is

x^2

Answer 5

What now is the second step?

Answer 6

add two times the starting number

Answer 7

yes, in terms of x ...

Answer 8

huh?

Answer 9

x is the starting number. The first step is that number squared. That is:
\[ x^2 \]

Answer 10

Using x, the starting number, what now is the next step?

Answer 11

2(x^2)?

Answer 12

No. You need to add 2 times the starting number.

What is just 2 times the starting number, in terms of x?

Answer 13

you dont make sense!

Answer 14

It's
\[ 2x \]

Answer 15

for step one or step two

Answer 16

We have x^2 from step one. And step two says now add 2 times the starting number, i.e., 2x.

So what do we have as an algebraic expression after step 2. That is, step 1 and 2.

Answer 17

so for step 2 i need to write x^2+ 2x

Answer 18

Yes.

Now step 3?

Answer 19

yes

Answer 20

How do you do it? I'm asking you. I know, I want to see if you get the idea now.

Answer 21

so next is going to be x^2+2x over x
?

Answer 22

yes

Answer 23

and that expression simplifies to what?

Answer 24

x^1+2

Answer 25

Yes, or just x + 2.

Ok, now step 4....

Answer 26

(a different problem) Example:
Step 1: Take some number and take the square root of it:
(let's call this number x) so we need the square root of x:
\[\sqrt{x}\]
Step 2: Subtract a half of the starting number
\[- \frac{1}{2} \cdot x\]
Step 1 together with Step 2:
so far we have
\[\sqrt{x}-\frac{1}{2}x\]

Step 3: Multiply the result by your starting number:
\[x(\sqrt{x}-\frac{1}{2}x)\]

Step 4: add your starting number
\[+x\]

Step 3 together with Step 4:
\[x(\sqrt{x}-\frac{1}{2}x)+x\]

Answer 27

before we do step 4 , how do i know i need to simplify

Answer 28

Because you always should if you can.

Answer 29

It's a general rule in mathematics

Answer 30

But if you're nervous about it, don't.

Answer 31

this just made me feel so dumb :D lol.
okay step 4: x+2-x

Answer 32

and that simplifies to .... what?

Answer 33

2?

Answer 34

Yes. Just 2.

Answer 35

all this work just for the number two -_- oh lord.

Answer 36

So in summary:
\[{x^2 + 2x \over x} - x \ = \ 2\]

Answer 37

and that will =2 for any number except for x=0

Answer 38

The object of the question obviously isn't to write down "2", but to show you how these things are done.

And the fact that it does reduce to 2 is actually the teacher/book's way of telling you you've got it right, because the final answer is so simple.

Sadly this isn't the case in real life, but it's great that it is when you're learning ;-)

Answer 39

true. thanksss:D