Simplifying (x+3)1/2 - (x+3)3/2 Expression

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Discussion Overview

The discussion revolves around simplifying the expression (x+3)^(1/2) - (x+3)^(3/2). Participants explore various approaches to the simplification process, including the use of exponent rules and algebraic manipulation.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant expresses confusion about how to simplify the expression and attempts to factor out (x+3)^(1/2).
  • Another participant confirms the approach and suggests using the property of exponents to subtract powers.
  • A participant calculates that 3/2 minus 1/2 equals 1, leading to the conclusion that the expression simplifies to 1.
  • Further clarification is provided that the result of the exponent subtraction gives (x+3)^(1), which is equivalent to (x+3).
  • Participants continue to simplify the expression to (x+3)^(1/2) [1 - (x + 3)].
  • One participant arrives at the expression (x+3)^(1/2) [-x + 2] as part of the simplification process.
  • Another participant confirms the final expression as (-x-2)(x+3)^(1/2) after further simplification.

Areas of Agreement / Disagreement

Participants generally agree on the steps taken to simplify the expression, but there is some uncertainty regarding the final form of the answer, with slight variations in how they express the final result.

Contextual Notes

Some steps in the simplification process may depend on the interpretation of exponent rules and algebraic manipulation, which could lead to different expressions being considered equivalent.

PaperStSoap
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Simplify

(x+3)1/2 - (x+3)3/2

i honestly am so lost on this one

how i approached it was

(x+3)1/2 [1 - ((x+3)3/2 / (x+3)1/2)]

but again, i have no idea what I'm doing.
 
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PaperStSoap said:
Simplify

(x+3)1/2 - (x+3)3/2

i honestly am so lost on this one

how i approached it was

(x+3)1/2 [1 - ((x+3)3/2 / (x+3)1/2)]

but again, i have no idea what I'm doing.

You're doing it correctly.

Now you need to use the fact that [math]\frac{x^a}{x^b}=x^{a-b}[/math]. Here you have the same term, (x+3), both the numerator and denominator so you can subtract the powers. What do you get once you do that?
 
Jameson said:
You're doing it correctly.

Now you need to use the fact that [math]\frac{x^a}{x^b}=x^{a-b}[/math]. Here you have the same term, (x+3), both the numerator and denominator so you can subtract the powers. What do you get once you do that?

well 3/2 minus 1/2 equals 1. so wouldn't [(x+3)/(x+3)] = 1?
 
PaperStSoap said:
well 3/2 minus 1/2 equals 1. so wouldn't [(x+3)/(x+3)] = 1?

Almost. You do get 1, but that's the new power. So you get
[math]\frac{(x+3)^{\frac{3}{2}}}{(x+3)^{\frac{1}{2}}}=(x+3)^{\frac{2}{2}}=(x+3)^1=(x+3)[/math]
 
so that would come out to

(x+3)^1/2 [1 - (x + 3)]
 
PaperStSoap said:
so that would come out to

(x+3)^1/2 [1 - (x + 3)]

Exactly. Now just simplify [1-(x+3)] and you're done.
 
(x+3)^1/2[-x+2] ?
 
PaperStSoap said:
(x+3)^1/2[-x+2] ?

[math]1-(x+3)=1-x-3=-x-2[/math] so final answer is

[math](-x-2)\sqrt{x+3}[/math]
 
man i can't believe i messed that one up
so final answer is
(x+3)^1/2 (-x-2)
 

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