數學功課一問2

1.
2X既2次方+7X+3
-------------------------
2X既2次方-7X-4
(2x+1)(x+3)
=-----------------
(2x+1)(x-4)

2.
Y既2次方-25
----------------------
Y既3次方-125
(y-5)(y+5)
=------------------------
(y-5)(y^2+5y+25)
(y+5)
=------------------
(y^2+5y+25)

3. Question misprinted.

4. Question misprinted.

5.
b a
--- - ---
a b
--------------
1 1
--- - ---
a b

b a
= -------
11

6.
y既-1次方+X既-1次方
--------------------------------
(xy)既-1次方

= (xy)(y既-1次方+X既-1次方)
= x + y

7. Question misprinted.

8.
2ac+bc-6ad-3bd
---------------------------
6ac+2ad+3bc+bd

c(2a+b) - 3d(2a+b)
=---------------------------
3c(a+b) + d(2a+b)

(c-3d)(2a+b)
=-------------------
(3c+d)(2a+b)

(c-3d)
=---------
(3c+d)

Rationalize the denominator

1. √t+5
---------
√t-5

(√t+5)^2
= --------------------
(√t-5)(√t+5)

(√t+5)^2
= ---------------
t - 25

2. √t-4
---------
√t+4

(√t-4)^2
= -------------------
(√t+4)(√t-4)

(√t-4)^2
= -------------
t - 16

3. 81X既2次方-16y
----------------------------------
3√x - 2√y

(81X^2-16y)(3√x - 2√y)
= ---------------------------------------
(3√x - 2√y)(3√x + 2√y)

(9x-4√y)(9x+4√y)(3√x - 2√y)
= ---------------------------------------
(9x - 4y)


Note, if the question is:
3. 81X既2次方-16y既2次方
----------------------------------
3√x - 2√y

then the answer becomes
(9x-4y)(9x+4y)(3√x - 2√y)
= ---------------------------------------
(9x - 4y)

= (9x+4y)(3√x - 2√y)