1. ## 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)

2. Originally Posted by vc15ao4
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!
$\displaystyle S = 2(hw + hl + wl)$

$\displaystyle S = 2hw + 2hl + 2wl$

$\displaystyle 2hw + 2hl = S - 2wl$

$\displaystyle 2h(w + l) = S - 2wl$

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

Originally Posted by vc15ao4
2) Solve for P---- A=P+ Prt
$\displaystyle A = P + Prt$

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

-Dan

3. Originally Posted by vc15ao4
3) Solve the equation (4/4x+9)+ (7/4x-9)= 44x+27/16x^2-81
I presume this equation is
$\displaystyle \frac{4}{4x + 9} + \frac{7}{4x - 9} = \frac{44x + 27}{16x^2 - 81}$

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

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

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

$\displaystyle 4(4x - 9) + 7(4x + 9) = 44x + 27$

$\displaystyle 16x - 36 + 28x + 63 = 44x + 27$

$\displaystyle 16x + 28x - 44x = 27 + 36 - 63$

$\displaystyle 0 \cdot x = 0$

or
$\displaystyle 0 = 0$

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

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

-Dan

4. dan u messed up on question #1..you forgot to add 2wl add the end of the first step

5. Originally Posted by vc15ao4
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
$\displaystyle \frac{2}{5x + 4} - \frac{4}{10x + 8}$
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.
$\displaystyle \frac{2}{5x + 4} - \frac{4}{10x + 8}$

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

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

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

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

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

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

-Dan

6. Originally Posted by vc15ao4
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

7. 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?

8. Originally Posted by vc15ao4
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

9. 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

10. Originally Posted by vc15ao4
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:

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

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

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

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

-Dan

11. 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?

12. never mind Dan, thanks a lot for your help...

13. Originally Posted by vc15ao4
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