Can you help me simplify the following?

Question

Plz show ur work. I have finals nxt week and wanna c how to do it....thnx

h+3 (over)
h^2-h-12


-48w (over)
16w^2-40w




AGAIN SHOW WORK plz =))

Answer 1

I hope you spell better on your finals.

For the first one, you'll have to factor the denominator, that's h^2-h-12. Start by drawing two sets of parentheses:

(h ) (h )

I put in the h's because h*h = h^2, the first part of the trinomial.

Now, you have to think of two numbers that, when multiplied, equal -12, and when added together, equal -1, the middle part of the trinomial. Can you think of any?

I can think of two: -4 and +3. So put those in your parentheses.

(h+3)(h-4)

Now here is what your newly factored expression will look like:
h+3 (over)
(h+3)(h-4)

You can cancel out (h+3). Replace them both with 1, because (h+3)/(h+3) = 1/1

Here is the answer:

1/(h+3)

For the second one, start out by canceling w.

-48w (over)
16w^2-40w

This becomes:

-48
16w - 40

Now, think of a number that is a factor of 48, 16, and 40.

8 is such a factor. So divide all the numbers by 8.

-6
2w - 5

And there's your answer. I hope this helps. Be sure to do similar problems from your book, as it takes practice to learn to factor things.

Answer 2

h+3
--------
h^2 - h - 12

The trick to this is that in order to "simplify"
something must cancel out at the top and bottom.
Since "h+3" is at the top, this is a "clue" that
you can probably factor the bottom into
(h +3) and something else, so the h + 3 cancels:

h + 3
-----------
(h + 3)(h - 4)

So if you cancel h + 3 on top and bottom:

1
----
h - 4

Now check your work.
Pretend h = "2"
and plug into the "original" fraction and
also into your reduced fraction to see if the value comes
out the same both times:

"2" + 3
-----------
4 - 2 - 12

5
---
-10

or - 1 / 2
This is the same as plugging h = "2"
into your reduced fraction to test it:

1
----
2 - 4
also equals - 1 / 2
==================================

For the next one, start looking for common factors
in top and bottom, both the "constants" and the "variables"

- 48w
--------
16w^2 - 40w

- 48 w
----------
w (16w - 40)

cancel out the w to leave

- 48
-------
16w - 40

8 * ( -6 )
------------
8 * ( 2w - 5 )

Cancel out the 8's on top and bottom to leave

- 6
--------
2w - 5

Check your work.
Try w = "2" to see if the first and last fraction
are equivalent expressions (values should come out the same)

- 48 (2 )
------------
64 - 80

- 96
--------
- 16

equals 6
compare with:

- 6
-------
4 - 5

- 6
-----
- 1

also equals 6

If you had a sign, arithmetic or algebraic error,
this would not have come out to be the same answer.

So this looks correct, but you can check again
using w = "1" or w = "3" etc. on a calculator.

P.S. On your test, if you write out your notes,
such as factoring out the "8" and writing these down
before canceling them out, then it is easier and faster
to go back and check your work later for errors. If you
don't write notes as to what you simplified and canceled,
then when you go back you have to do that all over again
in your head and could make more mistakes. So that is
why I recommend "factoring" out first, and writing this down, to show the "8" on top and bottom (or the "w" on top and bottom) before canceling these out.

If you check your work and mark the answers you have already confirmed with a [ box ], to mean you are sure these are done correctly, then you can mark the problems you are not sure about with a "circle" or "?" and go back and review, correct, or check those until all your answers have a [ box ].

This will help you keep track of your work, prioritize and focus, so you can concentrate on finding and fixing the errors
until everything checks out.

Answer 3

(h+3)/(h^2-h-12)
(h+3)/(h+3)(h-4)
1/(h-4)

(-48w)/(16w^2-40w)
(-6)(8w)/(2w-5)(8w)
-6/(2w-5)

Hope you do well on your finals.