Simplifying (x + 3/x - 1) + (4/1 - x) to a Constant: Easy Algebra Help

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Homework Help Overview

The discussion revolves around simplifying the expression (x + 3)/(x - 1) + 4/(1 - x) to determine if it results in a constant value. Participants are exploring algebraic manipulation and notation clarification.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to clarify the expression's notation and are discussing the simplification process. Some are questioning the validity of the answer provided in the answer book, while others are verifying their calculations.

Discussion Status

The discussion is ongoing, with participants expressing differing views on the correctness of the answer. Some have provided algebraic reasoning to support their conclusions, while others suggest using a calculator for verification.

Contextual Notes

There is confusion regarding the notation and the interpretation of the expression, as well as discrepancies between participants' results and the answer book. The participants are also considering the implications of the question's phrasing regarding simplification to a constant.

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Easy algebra help!

Show that (x + 3/x - 1) + (4/ 1 - x) simplifies to a constant.


The answer is 3, but all I can get is 1. It's wracking my brain. ANYONE?
 
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Joza said:
Show that (x + 3/x - 1) + (4/ 1 - x) simplifies to a constant.


The answer is 3, but all I can get is 1. It's wracking my brain. ANYONE?

Do you mean (x+3)/(x-1)+4/(1-x) ? Put in the correct brackets.
 
Yes! Sorry I messed up my notation...
 
x-1 = -(1-x)
so (x+3)/(x-1)+4/(1-x)=(x+3)/(x-1)-4/(x-1)
denominators are equal- so can add numerator
=(x-1)/(x-1)=1

So I get the same answer.
 
?

The answer book says 3.
 
book is wrong.

(x+3)/(x-1)=-4/(1-x)=4/(x-1) putting 3 in for x,
6/2=4/2 ? is right.
 
Yup Book is definitely wrong. Its 1. The question was show that it simplifies to a constant, so either way its alrite.
 
For a question like this, you can easily check it with a calculator. Just pick any random value of x, and evaluate.
 

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