[2x^(2)-18]/[x^(4)-81]
3.Simplify each of the following expression.
a.[x^(2)-2x+1]/[3x^(2)+17x-28]除以{[1-x^(2)]/[-3x^(2)+25x-28]}
b.[(3m-21n)/(6m+12n)]^2除以{[m^(2)n-49n^(3)]/[2m^(2)+8mn+8n^(2)] 乘以{[m^(2)n^(2)]/m^(2)-7mn]}
4.Let P(x)=[x^(4)-1]/[x^(3)-1] and Q(x)={[x^(2)+1](x+1)}/[x^(2)+x+1].
Do P(x) and Q(x) represent the same rational function?Explain your answer.
5.Let a>b>0.A solid metal cuboid of base area[a^(3)-b^(3)]cm2 and height(a+b)cm is melted
and recast into a new solid cuboid.If the base area of the new cuboid is [a^(2)-b^(2)]cm2,express
the height of the new cuboid in terms of a and b.
6.Let P=x^(3)-x^(2)-20x and Q=x^(3)+3x^(2)-24x-80.Find the HCF of P and Q.
7.Let R=3x^(3)+2x^(2)+1 and S=3x^(3)-7x^(2)+3x-2.Find the LCM of R and S.
8.Let f(x)=36x^(2)-12x-24 and g(x)=f(x)+3x^(3)-34x^(2)+16
a.Find g(x).
b.Find the HCF of f(x) and v(x)
9.Let u(x)=3x^(3)-2x^(2)-19x-6 and v(x)=-x[u(x)-6x^(3)+16x^(2)+6x
a.Find v(x)
b.Find the LCM of u(x) and v(x)
10.Let f(x)=2x^(3)-x^(2)-x and g(x)=2x^(3)-3x^(2)+1
a.Find the value of g(1).Hence,factorize g(x)
b.Let P and Q be the HCF and LCM of f(x) and g(x) respectively.
i.Find P and Q.
ii.Are the results of f(x)g(x) and P x Q equal?Explain your answer.
11.Let R=x^(4)-y^(4) and S=x^(3)y-x^(2)y-xy^(3)+y^3
a.Find the HCF and LCM of R and S.
b.Using the results of (a),find R x S.
12.The HCF and LCM of two polynomials are x^(2)y and 3x^(3)y^(2)z respectively.If the first polynomial is x^(2)y^(2),
find the second polynomial.
13.The HCF and LCM of three polynomials are bc and a^(2)b^(4)c^(3) respectively.If the first and the second
polynomials are abc^(3) and a^(2)bc^(2) respectively,find the third polynomial.
14.The HCF and LCM of three polynomials P,Q and R are 6uv^(2) and 72u^(3)v^(3)w^(2) respectively,where P=12uv^(2)
and Q=24u^(2)v^(2)w^(2).Write down two possible polynomials of R.
唔該show埋steps，最好跟番平時考試的要求。
同埋Ed題目我真係唔識，所以先問，唔係因為懶而問，所以唔好誤會。
Maths ratinoal functions
2015-05-13 5:23 am
回答 (5)
2015-05-13 8:13 pm
✔ 最佳答案
1.All the root
2.
Without x=3
3a.
[x^(2)-2x+1]/[3x^(2)+17x-28]除以{[1-x^(2)]/[-3x^(2)+25x-28]}
=(x-1)(x-1)(3x-4)(x-7)/[(3x-4)(x+7)(1-x)(1+x)
=-(x-1)(x-7)/(1+x)
3b
[(3m-21n)/(6m+12n)]^2除以{[m^(2)n-49n^(3)]/[2m^(2)+8mn+8n^(2)] 乘以{[m^(2)n^(2)]/m^(2)-7mn]}
=(2mnn)(m-7n)(m-7n)(m+2)/[2n(m+2n)(m+2n)(m-7n)(m+7n)(m-7n)]
=1/(m+7n)
4.
P(x)=[x^(4)-1]/[x^(3)-1]
P(x)=(x^2 -1)(x^2 +1)/[(x-1)(x^2 +x+1)
P(x)=(x+1)(x-1)(x^1 +1)/[(x^2 +x+1)(x-1)
Q(x)={[x^(2)+1](x+1)}/[x^(2)+x+1]
They are not the same rational function because P(x) can not x=1
5.
A1/A2=(h1/h2)^2
(a^3 -b^3)/(a^2 -b^2)=[(a+b)/h2]^2
(a-b)(a^2+ab+b^2)/[(a-b)(a+b)]=[(a+b)/h]^2
(a^2 +ab+b^2)/(a+b)=(1/h2)^2
h2=[(a+b)/(a^2 +ab+b^2)]^0.5
6.
P=x^(3)-x^(2)-20x
P=x(x-5)(x+4)
Q=x^(3)+3x^(2)-24x-80
Q=(x-5)(x+4)(x+4)
HCF=(x-5)(x+4)
7
R=3x^(3)+2x^(2)+1
R=(x+1)(3x^2 -x+1)
S=3x^(3)-7x^(2)+3x-2
S=(x-2)(3x^2 -x+1)
LCM=(x+1)(x-2)(3x^2 -x+1)
8a
f(x)=36x^(2)-12x-24
g(x)=f(x)+3x^(3)-34x^(2)+16
g(x)=36x^2 -12x-24+3x^3 -34x^2 +16
g(x)=3x^3 +2x^2 -12x-8
8b
f(x)=12(3x^-x-2)
f(x)=12(x-1)(3x+1)
g(x)=(x-2)(3x+1)(x+2)
HCF=3x+1
9a
u(x)=3x^(3)-2x^(2)-19x-6
v(x)=-x[u(x)-6x^(3)+16x^(2)+6x]
v(x)=-x(3x^(3)-2x^(2)-19x-6-6x^3 +16x^2 +6x)
v(x)=x(3x^3 -14x^2 +13x+6)
9b
v(x)=x(x-3)(x-2)(3x+1)
u(x)=(x-3)(3x+1)(x+2)
LCM=x(x-3)(3x+1)(x-2)(x+2)
10a
g(1)=2-3+1
g(1)=0
g(x)=(x-1)(x-1)(2x+1)
10bi
f(x)=x(x-1)(2x+1)
P=HCF=(x-1)(2x+1)
Q=LCM=x(x-1)(x-1)(2x+1)
10bii
f(x)g(x)
=x(x-1)(2x+1)(x-1)(x-1)(2x+1)
=x(x-1)^3 (2x+1)^2
PQ
=(x-1)(2x+1)(x-1)(2x+1)(x)(x-1)
=x(x-1)^3 (2x+1)^2
11a
R=x^4 -y^4
R=(x^2 -y^2)(x^2 +y^2)
R=(x-y)(x+y)(x^2 +y^2)
S=(x^3)(y)-(x^2)(y)-(x)(y^3)+(y^3)
S=(x^2)(y)(x-1)-(y^3)(x-1)
S=y(x-1)(x^2-y^2)
S=y(x-1)(x-y)(x+y)
HCF=(x-y)(x+y)
LCM=y(x-1)(x-y)(x+y)(x^2 +y^2)
11b
RS
=(x-y)(x+y)(x^2 +y^2)(y)(x-1)(x-y)(x+y)
=y(x-y)^2 (x+y)^2 (x-1)(x^2 +y^2)
12
second polynomial=3x^3 z
13
third polynomial=(b^3)(c)(1/a)
14
R=1.5u^3 v^3
2015-05-14 1:51 am
無論如何，點都要多謝你的意見。我會好好咁反省下嫁啦
2015-05-13 9:19 pm
呢啲街站，唔理啱唔啱，實有人"袋住先"的。
2015-05-13 8:07 am
1 part 都唔夠1分 0.0
2015-05-13 02:04:12 補充：
的確係，
但有時覺得有時分數亦都有佢1定嘅推動力
0.0
2015-05-13 02:04:12 補充：
的確係，
但有時覺得有時分數亦都有佢1定嘅推動力
0.0
2015-05-13 8:03 am
精彩絕倫！！！！！！
2015-05-13 01:53:57 補充：
大家不嬲都知道分數同帖數唔係最大問題，時間同心機先係重要～
我就睇下邊個咁偉大。。。
2015-05-13 09:09:33 補充：
發問者說得對「無話一定要做晒先比分」
但我之前幾次提出過，回答者不會是這樣心態。
因為一個負責任的回答者，他/她不會打算答幾題就走了去，因為這像是開始了一件未完成的事，而且亦都會令其他網友不知應否答下去。
所以，到頭來就是會答題的機會大大減低，也令發問者浪費點數和等待的時間。
我的發言無意指責任何人又或者作什麼批評，其實只是客觀地指出一個事實，擔心發問者未必了解對方的想法而有所損失。
2015-05-13 09:12:08 補充：
就以 15 分於一個帖內問 15 題為例。
可以很容易想到效果～
比較一下 (5 分在一個帖問 5 題) × 3。
哪個會容易得到回應？
哪個會令更多網友有機會提供意見和解答？
哪個會令人看看就走？
2015-05-13 21:30:04 補充：
太客氣啦～
祝你學業進步！
╭∧---∧╮
│ .✪‿✪ │
╰/) ⋈ (\\╯
我在此答兩題吧：
補充第１題
The domain of a rational function is the set of x where the denominator is non-zero. That is, (x - 2)² + 3 ≠ 0, that is ALL real numbers ℝ, because (x - 2)² + 3 ≥ 3 > 0.
2015-05-13 21:31:05 補充：
補充第２題
(2x² - 18)/(x⁴ - 81)
= 2(x² - 9)/[(x²)² - 9²]
= 2(x² - 9)/[(x² + 9)(x² - 9)]
= 2/(x² + 9)
2015-05-13 01:53:57 補充：
大家不嬲都知道分數同帖數唔係最大問題，時間同心機先係重要～
我就睇下邊個咁偉大。。。
2015-05-13 09:09:33 補充：
發問者說得對「無話一定要做晒先比分」
但我之前幾次提出過，回答者不會是這樣心態。
因為一個負責任的回答者，他/她不會打算答幾題就走了去，因為這像是開始了一件未完成的事，而且亦都會令其他網友不知應否答下去。
所以，到頭來就是會答題的機會大大減低，也令發問者浪費點數和等待的時間。
我的發言無意指責任何人又或者作什麼批評，其實只是客觀地指出一個事實，擔心發問者未必了解對方的想法而有所損失。
2015-05-13 09:12:08 補充：
就以 15 分於一個帖內問 15 題為例。
可以很容易想到效果～
比較一下 (5 分在一個帖問 5 題) × 3。
哪個會容易得到回應？
哪個會令更多網友有機會提供意見和解答？
哪個會令人看看就走？
2015-05-13 21:30:04 補充：
太客氣啦～
祝你學業進步！
╭∧---∧╮
│ .✪‿✪ │
╰/) ⋈ (\\╯
我在此答兩題吧：
補充第１題
The domain of a rational function is the set of x where the denominator is non-zero. That is, (x - 2)² + 3 ≠ 0, that is ALL real numbers ℝ, because (x - 2)² + 3 ≥ 3 > 0.
2015-05-13 21:31:05 補充：
補充第２題
(2x² - 18)/(x⁴ - 81)
= 2(x² - 9)/[(x²)² - 9²]
= 2(x² - 9)/[(x² + 9)(x² - 9)]
= 2/(x² + 9)
收錄日期: 2021-04-15 20:09:18
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150512000051KK00064