# (1-2 / 1) × (1-1 / 3) × (1-1 / 4) ×.× How about (1-19) x (1-20)?

## (1-2 / 1) × (1-1 / 3) × (1-1 / 4) ×.× How about (1-19) x (1-20)?

It means to count out every bracket. That's it
Then equal to 1 ÷ 2 * 2 ÷ 3 * 3 ÷ 4
Multiply by one and divide by one
The last is 1 ÷ 20

### Calculation: (1 + 2 / 1) x (1 + 3 / 1) x (1 + 4 / 1) x... (1 + 99 / 1) x (1 + 100 / 1)

Original formula = 3 / 2 x 4 / 3 x 5 / 4....... X 100 / 99 x 101 / 100
=101/2
Because every two items are divided, only the denominator of the first item and the numerator of the last item are left

### Calculation: ① X-1 / x + 2 * x ^ 2-4 / x ^ 2-1 ② x ^ 2-3x + 2 / x ^ 2 + 3x + 2 * 3x + 3 / 2x-x ^ 2 ③ 2Ab a ^ 2-B ^ 2 * a ^ 2-ab-2b ^ 2 A ^ 2-2ab ④ x + y 12xy ^ 2 divided by x ^ 2-y ^ 2 4xy ⑤ (3b ^ 2 2a) ^ 2 divided by (- B a) ^ 3 ⑥ 2Ab divided by 2Ab 1 * 2B a ⑦2x x + 2 * x ^ 2 + 5x + 6 x ^ 3-3x ^ 2 divided by x ^ 2 + 2x-3-9x ⑧ x + y x ^ 2-4y ^ 2 divided by (x ^ 2-2xy) divided by x ^ 2-y ^ 2 + xy-2y ^ 2 calculation: Question 1: X-1 / x + 2 * x ^ 2-4 / x ^ 2-1 Question 2: x ^ 2-3x + 2 / 2 x ^ 2 + 3x + 2 * 3x + 2 / 3 x-x ^ 2 Question 3: A ^ 2-B ^ 2 of 2Ab * a ^ 2-ab-2b ^ 2 of a ^ 2-2ab Question 4: 12xy ^ 2 of X + y divided by 4xy of x ^ 2-y ^ 2 Question 5: (3b ^ 2a) ^ 2 divided by (- B / a) ^ 3 Question 6: 2Ab divided by 1 / 2Ab * A / 2B Question 7: 2x x + 2 * x ^ 2 + 5x + 6 x ^ 3-3x ^ 2 divided by x ^ 2 + 2x-3 x ^ 3-9x Question 8: x + Y / x ^ 2-4y ^ 2 divided by (x ^ 2-2xy) divided by x ^ 2-y ^ 2 / x ^ 2 + xy-2y ^ 2

⑴(x+2/x-1)* (x^2-1/x^2-4)
=（（x+2)*(x+1)*(x-1)）/（（x-1）*（x-2)*x+2)
=（x+1)/(x-2)
⑵(x^2+3x+2/x^2-3x+2)*(2x-x^2/3x+3)
=((x+1)*(x+2)*(-x)*(x-2))?((x-1)*(x-2)*3*(x+1)
=(-1/3)x(x+2)/(x-1)
⑶(a^2-b^2/2ab)*(a^2-2ab/a^2-ab-2b^2)
=((a+b)*(a-b)*a*(a-2b))/(2ab*(a-2b)*(a+b))
=(a-b)/(2b)
⑷(12xy^2/x+y)*(x^2-y^2/4xy)
=(12xy^2*(x+y)*(x-y))/(4xy*(x+y))
=3y*(x-y)
⑸[(2a/3b^2)^2]*[(-b/a)^3]
=[4a^2/9b^4]*[-b^3/a^3]
=-4a^2b^3/9a^3b^4
=-(4/9)*1/(ab)
⑹(x+2/2x)*(x^3-3x^2/x^2+5x+6)*(x^2+2x-3/x^3-9x)
=（(x+2）*x^2*（x-3)*(x+3)*(x-1))/(2x*(x+2)*(x+3)*x*(x-3)*(x+3))
=(1/2)*(x-1)/2(x+3)
⑺(x^2-4y^2/x+y)*(1/x^2-2xy)*(x^2-y^2/x^2+xy-2y^2)
=((x+2y)*(x-2y)*(x+y)*(x-y))/((x+y)*(x-2y)*x*(x+2y)*(x-y))
=1/x

### How to calculate X-1 / x + 1 minus x + 1 / 3x-3 = 2

(x+1)/(x-1)-3(x-1)/(x+1)=2
Multiply both sides by (x + 1) (x-1)
(x+1)^2-3(x-1)^2=2(x^2-1)
4x^2-8x=0
X = 2 or x = 0

3/（x+1）

3/(x+1)