Factorization of rational proper fraction How do you know it's decomposed like this? How can you tell the denominators? How to use the undetermined coefficient method to solve these problems?

x（x-1）²
The factors of are x, X-1, X (x-1), (x-1) ^ 2
But x (x-1) is not a true fraction, that is, it can also be decomposed into x and X-1, and these two factors are repeated with the above, so it is unnecessary to write (only the coefficient A.C changes)
This kind of problem can be solved by comparing coefficient after general division,
Multiply both sides by X (x-1) ^ 2
1=A(X-1)^2+BX+CX(X-1)
1=(A+C)X^2+(B-2A-C)X+A
therefore
A=1
A+C=0 C=-A=-1
B-2A-C=0
B=2A+C=2-1=1

Parallelogram ABCD, vertex a (0, - 9), B (2,6), C (4,5), find the coordinates of the fourth vertex D

Coordinates of point D: D (2, - 10)

Using derivative knowledge to judge the number of negative real roots of equation 3x-x2 = 0______ One

Let f (x) = 3x-x2, ∵ f (- 1) = - 23 ＜ 0, f (0) = 1 ＞ 0, and the image of ∵ function f (x) is continuous on [- 1,0], ∵ function f (x) has a zero point in (- 1,0), and ∵ function y = 3x increases, y = x2 decreases, ∵ function f (x) increases monotonically on (- ∞, 0), and ∵ function f (x) has only one zero point in (- 1,0), so the equation is stable 3x-x2 = 0 has only one negative real root, so the answer is 1

The distance from a point m on the parabola y = 4x square to the focus is

Parabola y = 4x square, m (XM, YM)
x^2=y/4=2py,p=1/8
The guide line is y = - P / 2 = - 1 / 16
The distance from the point to the focus is equal to the distance from the point to the guide line, that is: YM + P / 2 = YM + 1 / 16

Write out the solution of a positive integer of the quadratic equation 3x-2y = 5

This can have
x=3
y=2

The locus of a point in the plane whose sum of distances from two fixed points is equal to constant 2a is called ellipse. These two fixed points are called the focus of ellipse, and the distance between them is called the focal length of ellipse. Exercise 1: given that the coordinates of two fixed points are (- 4,0) and (- 4,0), respectively, and the sum of distances from the moving point P to two fixed points is equal to 8, then the locus of point P is & # 160;, # 160;, # 160;, # 160;, # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; # 160; &#Objective: to get the two fixed-point coordinates (- 4,0), (4,0) and the distance from the moving point P to two fixed points, the distance from the moving point P to two fixed points, the distance from the moving point P to two fixed points, and the sum of the sum of the two points is equal to 6, then the trajectory of P point is # # 35; 35; 35; 35\\\\35\\\\\\\\\\\\\\\\\\\\\\\\\\\#160;

Straight line, No

It is necessary to write a quadratic equation of one variable which can be solved by both square root method and factorization method___ ．

According to the meaning of the question can write equation: x2-64 = 0, so the answer can be: x2-64 = 0

How many days are there between May 20, 2011 and December 23, 2012

This year, there are still seven months, namely, 6.7.8, 9.10.11.12, with 214 days in total, 22 days in 12 years, and 20 days in this month (not counting today)
Add up to 256 days (today is not included), add up to 257 days

Four pens and five writing pens are 45 yuan in total, and five pens and four writing pens are 50 yuan in total. How much is a pen more expensive than a writing pen?
You can't solve equations without learning equations,

Two total price subtraction = 50-45 = 5 yuan = 5 steel pens - 4 pens + 4 Brushes - 5 brushes = 1 pen - 1 brush = 5 yuan
So a pen is 5 yuan more expensive than a writing brush

Since 2013, Xiao Li has deposited 1000 yuan at the end of each year for six consecutive years. If the annual interest rate is 6%, compounded annually, how much money can he withdraw after six years?
Since 2013, Xiao Li has deposited 1000 yuan at the end of each year for six consecutive years. If the annual interest rate is 6%, compounded annually, how much can he withdraw after six years? Please give the calculation formula and answer,

This is the calculation of the final value of an ordinary annuity. You can directly apply the formula as follows,
Sum of principal and interest at maturity = 1000 * ((1 + 6%) ^ 6-1) / 6% = 6975.32 yuan
Note: ^ is the power

Factorization of rational proper fraction How do you know it's decomposed like this? How can you tell the denominators? How to use the undetermined coefficient method to solve these problems?