Why is this equation correct? (algebraic fraction simplification)

  • Thread starter Anarcho
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    Fraction
In summary: This is when you take the number and reduce it down to the lowest number that will still allow the two fractions to be equal.I haven't heard that phrase before, but I will try reducing to a common denominator.This is the solution: In summary, when you are trying to solve a fraction, you reduce it to a common denominator by dividing numerator and denominator by the lowest number that will still allow the two fractions to be equal.
  • #1
Anarcho
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0
Homework Statement
Rearranging equation
Relevant Equations
z=((1+x)/(1+y)*a-a)/a)
Hi all,

I cannot figure out how I get to the alternate form. I really do need help here.
241576
241577

Not sure how this is done.
Thank you
 
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  • #2
First you simplify the fraction by dividing numerator and denominator by ##a##. Then you add the fraction to what's left in the numerator.
 
  • #3
I have the same problem. But both wolframalpha as well as my notes get to the same conclussion. (scratching my head)
 
  • #4
Anarcho said:
I have the same problem. But both wolframalpha as well as my notes get to the same conclussion. (scratching my head)
Have you tried it? Start by trying to simplify out the ##a##.
 
  • #5
DrClaude said:
No, this is not what you get.
You're right. I'm going to delete my post. Bonehead mistake on my part...
 
  • #6
Mark44 said:
You're right. I'm going to delete my post. Bonehead mistake on my part...
It happens even to the best of us :smile:
 
  • #7
Anarcho said:
I have the same problem. But both wolframalpha as well as my notes get to the same conclussion. (scratching my head)
I have deleted my earlier post, since my thinking was incorrect. Follow the hints given by @kuruman and @DrClaude.
 
  • #8
DrClaude said:
Have you tried it? Start by trying to simplify out the aa.

I get ##((x+1)/(y+1))−1##
 
  • #9
Anarcho said:
I get (x+1)/(y+1)-1
Simplify some more. Hint: ##-1 = -\frac{y+1}{y+1}.##
 
  • #10
And why is that? This might be the problem I don't understand it
 
  • #11
Anarcho said:
And why is that? This might be the problem I don't understand it
Are you saying you don't understand why a number divided by itself is equal to ##1##?
 
  • #12
:sorry::sorry::sorry: I must look like an idot. Now I get it.
 
  • #13
Anarcho said:
:sorry::sorry::sorry: I must look like an idot. Now I get it.
We all have our blind spots here and there. :oldsmile:
 
  • #14
Anarcho said:
I get ##((x+1)/(y+1))−1##
Have you ever heard the term "reducing to a common denominator?"
 

1. Why do we need to simplify algebraic fractions?

Simplifying algebraic fractions allows us to express them in their simplest form, making it easier to solve equations and work with expressions. It also helps us to identify common factors and eliminate unnecessary terms.

2. How do we know if an equation is simplified?

An equation is considered simplified when all common factors have been canceled out and there are no more like terms that can be combined.

3. What are the basic steps for simplifying algebraic fractions?

The basic steps for simplifying algebraic fractions are: 1) Factor both the numerator and denominator, 2) Cancel out any common factors, 3) Multiply any remaining factors in the numerator and denominator, and 4) Simplify the resulting fraction, if possible.

4. Can we simplify algebraic fractions with variables?

Yes, we can simplify algebraic fractions with variables by following the same steps as simplifying fractions with numbers. We just need to be careful to only cancel out common factors and not any terms with different variables.

5. Why is it important to check our work when simplifying algebraic fractions?

It is important to check our work when simplifying algebraic fractions to ensure that we have not made any errors and that the resulting fraction is in its simplest form. This helps us to avoid mistakes and have confidence in our solutions.

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