The correct answer is C: 1/(x + 4)(x - 5)
Why? Well, let's first simplify x^2 - 3x - 10 and x^2 + x - 12; the two denominators. Each of these should become an (x +/- number), and to figure out the number, as well as whether it is positive or negative, we can do a simple trick
Look at the factors of the right number (In this case, -10 and -12)
-10 -12
1 * -10 1 * -12
-1 * 10 -1 * 12
-2 * 5 -2 * 6
2 * -5 2 * -6
-3 * 4
4 * -3
Now for part 2
Which of these pairs add up to the middle number? One of the pairs of -10 should make -3, and likewise, one of the pairs of -12 should make 1 (when x has no number in front of it you may safely assume it is 1).
2 - 5 = -3 and 4 - 3 = 1, so we now know that the 2 fraction equations simplified is
x + 2 / (x + 2)(x - 5) * x - 3/(x -3)(x + 4)
Notice anything repeating? As long as they are apart of the same fraction, we can cross out anything that has the same x - number. Crossing out both x + 2 and x - 3, we now simply have x - 5 * x + 4. Because we crossed out both numerators, the top numbers both become 1, thus giving our answer, C.
If you convert the fractions to ___/20 then you will see. Here; 2/5 = 8/20. 1/4 = 5/20. I hope this helps.
Answer:
See below.
Step-by-step explanation:
13. D
Simply subtract. 85376 - 37793 = 47583.
14. C
[Something] - 32497 = 26348
Add 32497 to both sides:
[Something] - 32497 + 32497 = 26438 + 32497
[Something] = 58845
15. C
Compute each difference:
A: 51455 - 26478 = 24977
B: 49351 - 15274 = 34077
C: 63286 - 37439 = 25847
(D: 46307 - 21550 = 24757)
16. B
Simply subtract:
143864 - 112955 = 30909
17. A
First, find the difference:
85732 - 39864 = 45868
Only 45798 (A) is less than 45868.
(Note that B is equal to, not less than).
18. C
Subtract:
45932 - 29574 = 16358.
19. B
Subtract:
96834 - 31727 = 65107 - 12156 = 52951
20. C
27301 - 12352 - [Something] = 7356
14949 - [Something] = 7356
Add [Something] to each side:
14949 = 7356 + [Something]
Subtract 7356 from each side.
7593 = [Something]
Note: Do you need help with subtraction specifically? These questions can be solved with simply with a calculator, but perhaps that is not the intention here. Anyways, I recommend using Khan Academy to improve your arithmetic skills if necesary.
Supplementary angles are those which sum upto 180°
Complementary are those which sum to 90°
so if you know one angle, you can find other.
