General score: (1) 1 / A + 1,3 / 1-A, 5 / A ^ 2-1 (2) a / A ^ 2-4, A-1 / A-2, a + 2 / A ^ 2-4a + 4

General score: (1) 1 / A + 1,3 / 1-A, 5 / A ^ 2-1 (2) a / A ^ 2-4, A-1 / A-2, a + 2 / A ^ 2-4a + 4

(1)1/a+1=(a-1)/(a+1)(a-1)
3/1-a=-3(a+1)/(a+1)(a-1)
5/a^2-1 =5/(a+1)(a-1)
(2)a/a^2-4=a(a-2)/(a+2)(a-2)²
a-1/a-2=(a-1)(a+2)(a-2)/(a+2)(a-2)²
a+2/a^2-4a+4=(a+2)²/(a+2)(a-2)²

7 out of 15 and 9 out of 20, 5 out of 8 and 7 out of 24, 8 out of 15 and 7 out of 16 ask the great God for help

7 of 15 and 9 of 20, 7 / 15 = 28 / 60, 9 / 20 = 27 / 60, 5 of 8 and 7 of 24, 5 / 8 = 15 / 24, 7 / 24 = 7 / 24, 8 of 15 and 7 of 16 = 128 / 240, 7 / 16 = 105 / 240

From the integers from 1 to 100, find 10 numbers and make their reciprocal sum equal to 1

1.
1=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9
-1/10+1/10
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
+(1 / 7-1 / 8) + (1 / 8-1 / 9) + (1 / 9-1 / 10) + 1 / 10 each two are divided into a group
=1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/10
This is the elimination of column terms in a sequence

Nineteen and eighteen seventeen times minus nine equals nine

-171.85

How to calculate 14 out of 17 + 14 out of 17 * 16 with a simple method

14/17＋14/17×16
＝14/17×﹙1＋16﹚
＝14/17×17
＝14.

Factorization ax ^ 2 + BX ^ 2-A ^ 2x-b ^ 2x-2abx + A ^ 2B + AB ^ 2

Original formula = (a + b) x ^ 2 - (a ^ 2 + B ^ 2 + 2Ab) x + AB (a + b)
=(a+b)x^2-(a+b)^2x+ab(a+b)
=(a+b)[x^2-(a+b)x+ab]
=(a+b)(x-a)(x-b)

25 out of 15 minus 5 out of 16

25/15-5/16
=5/3-5/16
=80/48-15/48
=65/48
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Use a 64 cm long wire to form a 6 cm long and 5 cm wide rectangular teaching aid. What is the maximum height of this teaching aid?
Make a list!

It's 64-4-6-5 = 5cm

A number divided by 16, 23, 37, the remainder is 2, what is the maximum number
It's the remainder

The maximum number is 7
Because 16, 23 and 37 minus 2 are 14, 21 and 35 respectively, the greatest common divisor of these three numbers is 7

Let {CN} satisfy CN = 2 / (3N ^ 2 + 3n), find the first n terms and TN of {CN}

This kind of problem is the first n terms and TN = C1 + C2 + C3 +. + CN  TN = (2 / 3) * [1 / 2 + 2-1 / 3 + 1 / 3 + 1 / 3 + 1 / 3 + 1 / n-1 / (n + 1)] = (2 / 3) * [1 / n-1 / (n + 1)] of CN = 2 / (3N ^ 2 + 3n) = (2 / 3) / [n (n + 1)] = (2 / 3) = [1-1 / 2 + 1 / 2-1 / 3 + 1 / 3-1 / 4 + 1 / n-1 / (n + 1)] = (2 / 3) * [1