AlvinReyes995
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How can I simplify these fractions?
- Thread starter AlvinReyes995
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- Nov 24, 2012
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Hello and welcome to FMH! 
Generally, we want to factor the numerators and denominators, and then divide out any factors common to both. Let's begin with a). I would observe that:
[MATH]\frac{x^3-1}{1-x^5}=-\frac{x^3-1}{x^5-1}[/MATH]
And:
[MATH]x^3-1=(x-1)(x^2+x+1)[/MATH]
[MATH]x^5-1=(x-1)(x^4+x^3+x^2+x+1)[/MATH]
Can you proceed?
Generally, we want to factor the numerators and denominators, and then divide out any factors common to both. Let's begin with a). I would observe that:
[MATH]\frac{x^3-1}{1-x^5}=-\frac{x^3-1}{x^5-1}[/MATH]
And:
[MATH]x^3-1=(x-1)(x^2+x+1)[/MATH]
[MATH]x^5-1=(x-1)(x^4+x^3+x^2+x+1)[/MATH]
Can you proceed?