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Math Help - rewriting expressions

  1. #1
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    rewriting expressions

    I have a few homework questions that I just don't understand. It would be greatly appreciated if you show me step by step how you got them, thank you very much!!

    1) Solve for H--- S= 2(hw+hl+wl)

    2) Solve for P---- A=P+ Prt

    3) Solve the equation (4/4x+9)+ (7/4x-9)= 44x+27/16x^2-81

    4) Solve the equation (2/5x+4)-(4/10x+8)
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vc15ao4 View Post
    1) Solve for H--- S= 2(hw+hl+wl)
    Please note that the variable H and the variable h are usually not the same thing!
    S = 2(hw + hl + wl)

    S = 2hw + 2hl + 2wl

    2hw + 2hl = S - 2wl

    2h(w + l) = S - 2wl

    h = \frac{S - 2wl}{2(w + l)}


    Quote Originally Posted by vc15ao4 View Post
    2) Solve for P---- A=P+ Prt
    A = P + Prt

    Similar to the above. Factor the P on the right hand side, then divide by the factor that remains. For reference I get:
    P = \frac{A}{1 + rt}

    -Dan
    Last edited by topsquark; September 5th 2007 at 02:16 PM. Reason: Fixed it up.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vc15ao4 View Post
    3) Solve the equation (4/4x+9)+ (7/4x-9)= 44x+27/16x^2-81
    I presume this equation is
    \frac{4}{4x + 9} + \frac{7}{4x - 9} = \frac{44x + 27}{16x^2 - 81}
    (Please be more careful in your use of parenthesis!)

    First you want to get a common denominator for all terms. In this case it is going to be simple because
    (4x + 9)(4x - 9) = 16x^2 - 81

    So
    \frac{4}{4x + 9} \cdot \frac{4x - 9}{4x - 9} + \frac{7}{4x - 9} \cdot \frac{4x + 9}{4x + 9} =  \frac{44x + 27}{16x^2 - 81}

    \frac{4(4x - 9) + 7(4x + 9)}{16x^2 - 81} =  \frac{44x + 27}{16x^2 - 81}<-- Now multiply both sides by 16x^2 - 81:

    4(4x - 9) + 7(4x + 9) = 44x + 27

    16x - 36 + 28x + 63 = 44x + 27

    16x + 28x - 44x = 27 + 36 - 63

    0 \cdot x = 0

    or
    0 = 0

    So it looks like any value of x will solve the equation, since both sides are already equal. BUT, look at the original equation:
    \frac{4}{4x + 9} + \frac{7}{4x - 9} = \frac{44x + 27}{16x^2 - 81}

    From here it is clear that we are restricted by the denominators: we must not have x = \pm \frac{9}{4}. Other than that, the solution is any x.

    -Dan
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  4. #4
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    dan u messed up on question #1..you forgot to add 2wl add the end of the first step
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vc15ao4 View Post
    I
    4) Solve the equation (2/5x+4)-(4/10x+8)
    Same comment about the parenthesis as I made above. If this is supposed to be
    \frac{2}{5x + 4} - \frac{4}{10x + 8}
    you need to write it as 2/(5x + 4) - 4/(10x + 8).

    This is not an equation, so it cannot be solved. I presume the question is to perform the indicated operation.
    \frac{2}{5x + 4} - \frac{4}{10x + 8}

    Note that 10x + 8 = 2(5x + 4), thus
    = \frac{2}{5x + 4} \cdot \frac{2}{2} - \frac{4}{10x + 8}

    = \frac{4}{10x + 8} - \frac{4}{10x + 8}

    = \frac{4 - 4}{10x + 8}

    = \frac{0}{10x + 8}

    = 0 \left ( \text{so long as }x \neq -\frac{5}{4} \right )

    (Your Math teacher likes, zeros doesn't (s)he?)

    -Dan
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vc15ao4 View Post
    dan u messed up on question #1..you forgot to add 2wl add the end of the first step
    So I did. Thanks for the spot!

    -Dan
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  7. #7
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    dan, I don't know why but for the two questions where the answer is 0, my computer isn't accpeting it as right. THe homework is online, and every time I type in 0 or zero, it says incorrect?
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vc15ao4 View Post
    dan, I don't know why but for the two questions where the answer is 0, my computer isn't accpeting it as right. THe homework is online, and every time I type in 0 or zero, it says incorrect?
    I don't know what to tell you about number 3. I just plugged it into my calculator and the calculator agrees. However note that the answer here is not x = 0, it is any x such that x is not 4/9 or -4/9. I don't know how you would plug that into the computer.

    As far as number 4 is concerned, you originally told me to "solve the equation." Did you leave something out of the problem?

    -Dan
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  9. #9
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    can u give me a brief review of all the questions and cleary state what the answers are, I'm still a little confused dan..thanks again
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  10. #10
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vc15ao4 View Post
    can u give me a brief review of all the questions and cleary state what the answers are, I'm still a little confused dan..thanks again
    Now I'm confused. Re-reading the posts will give you the answer you seek:

    Quote Originally Posted by topsquark View Post
    Please note that the variable H and the variable h are usually not the same thing!
    S = 2(hw + hl + wl)

    h = \frac{S - 2wl}{2(w + l)}
    Quote Originally Posted by topsquark View Post
    A = P + Prt

    P = \frac{A}{1 + rt}
    Quote Originally Posted by topsquark View Post
    I presume this equation is
    \frac{4}{4x + 9} + \frac{7}{4x - 9} = \frac{44x + 27}{16x^2 - 81}

    We must not have x = \pm \frac{9}{4}. Other than that, the solution is any x.
    Quote Originally Posted by topsquark View Post
    \frac{2}{5x + 4} - \frac{4}{10x + 8}
    = 0 \left ( \text{so long as }x \neq -\frac{5}{4} \right )
    I'm not sure what more I can say to make the final answers clearer...

    -Dan
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  11. #11
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    dan, thanks again, but the last thing I will ask is that I notified u that you messed up on number 1, but still gave me the same answer from back when u messed up?
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  12. #12
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    never mind Dan, thanks a lot for your help...
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  13. #13
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vc15ao4 View Post
    dan, thanks again, but the last thing I will ask is that I notified u that you messed up on number 1, but still gave me the same answer from back when u messed up?
    No, I changed the original post that I had made. The missing 2 is where it should be.

    -Dan
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