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Math Help - How to complete these problems?

  1. #1
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    How to complete these problems?

    I'm having difficulties solving the following problems, I would very much appreciate it if someone could show me how to solve them step-by-step.

    Add or Subtract as indicated and simplify.

    14. (x)/(x +3) + (3)/(x +3)

    15. (a^2 - 1)/(a - 1) - (a - 1)/(a + 1)

    16. (1)/(x) - (3)/(x+2) - (6)/(x^2 + 2x)

    Multiply or divide as indicated and simplify.

    17. (x^2 + x - 20)/(x^2 - 16) times (x^2 - 25)/(x - 5)

    18. (x + 2)/(x^2 + 2x + 1) divided by (x^2 - 4)/(x + 1)
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  2. #2
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    Quote Originally Posted by Quincy Goss View Post
    I'm having difficulties solving the following problems, I would very much appreciate it if someone could show me how to solve them step-by-step.

    Add or Subtract as indicated and simplify.

    14. (x)/(x +3) + (3)/(x +3)

    15. (a^2 - 1)/(a - 1) - (a - 1)/(a + 1)

    16. (1)/(x) - (3)/(x+2) - (6)/(x^2 + 2x)

    Multiply or divide as indicated and simplify.

    17. (x^2 + x - 20)/(x^2 - 16) times (x^2 - 25)/(x - 5)

    18. (x + 2)/(x^2 + 2x + 1) divided by (x^2 - 4)/(x + 1)
    HI

    (14) \frac{x}{x+3}+\frac{3}{x+3}=\frac{x+3}{x+3}=1

    (15) \frac{a^2-1}{a-1}-\frac{a-1}{a+1}

    =\frac{(a+1)(a-1)}{a-1}-\frac{a-1}{a+1}

    =\frac{(a+1)^2-(a-1)}{a+1}

     <br />
=\frac{a^2+2a+1-a+1}{a+1}<br />

    Then continue simplifying , i think you can try (16)

    For (17) , \frac{x^2+x-20}{x^2-16}\times\frac{x^2-25}{x-5}

    \frac{(x+5)(x-4)}{(x+4)(x-4)}\times\frac{(x+5)(x-5)}{x-5}

    do some appropriate cancellings , then simplify .

    Now try (18) .
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  3. #3
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    Thanks so much!
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  4. #4
    MHF Contributor
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    Talking

    Quote Originally Posted by Quincy Goss View Post
    I'm having difficulties solving the following problems, I would very much appreciate it if someone could show me how to [simplify] them step-by-step.
    Ouch! They were supposed to have covered this material in the book and / or in class before assigning homework on them!

    To learn, in general, how to work these exercises, try some online lessons:

    . . . . .Google results for "adding rational expressions"

    . . . . .Google results for "multiplying rational expressions"

    Have fun!
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