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Thread: simply algeberic fraction

  1. #1
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    simply algeberic fraction

    express  \frac{x+1}{3x^{2}-3} - \frac{1}{3x+1}

    as a single fraction in its simplest form.

    I got  \frac{4x+4}{3x^{3} + 9x^{2} + 9x -3} but thats not the correct answer, can someone show me hot to get to  \frac{4}{3(x-1)(3x+1)}

    thank you.
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  2. #2
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    Quote Originally Posted by Tweety View Post
    express  \frac{x+1}{3x^{2}-3} - \frac{1}{3x+1}

    as a single fraction in its simplest form.

    I got  \frac{4x+4}{3x^{3} + 9x^{2} + 9x -3} but thats not the correct answer, can someone show me hot to get to  \frac{4}{3(x-1)(3x+1)}

    thank you.
    hi

    \frac{(x+1)(3x+1)-(3x^2-3)}{3(x^2-1)(3x+1)}

    \frac{3x^2+x+3x+1-3x^2+3}{3(x+1)(x-1)(3x+1)}

    \frac{4x+4}{3(x+1)(x-1)(3x+1)}

    what do u see in common for the numerator ?
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  3. #3
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    Quote Originally Posted by mathaddict View Post
    hi

    \frac{(x+1)(3x+1)-(3x^2-3)}{3(x^2-1)(3x+1)}

    \frac{3x^2+x+3x+1-3x^2+3}{3(x+1)(x-1)(3x+1)}

    \frac{4x+4}{3(x+1)(x-1)(3x+1)}

    what do u see in common for the numerator ?
    Is that the correct answer? And is that the same as my answer but simplified?
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  4. #4
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    Quote Originally Posted by Tweety View Post
    Is that the correct answer? And is that the same as my answer but simplified?
    its not fully simplified , i left the last step for you , note that 4x+4=4(x+1)

    so when you cancel the x+1 , you will get the answer in your book
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