# Calculate (square of x-x-6) ÷ (x-3)

## Calculate (square of x-x-6) ÷ (x-3)

(square of X - X-6) ÷ (x-3)
=（x+2)(x-3）÷（x-3）
=x+2

### Calculate the square of (2x-6) / X - 4x + 4 ÷ (x + 3) × (square of X + X-6) / (3-x) (x + 3) and (square of X + X-6) are two formulas!

Original formula = 2 (x-3) / [(X-2) ^ 2] * 1 / (x + 3) * (x + 3) (X-2) / (3-x)
=-2/(x-2)

### Calculate the square of X-5 / 1-x - 6-10 / 25 + 2x / x + 1

=1/(x-5)-6/(x+5)(x-5)-(x+1)/2(x+5)
=2(x+5)/2(x+5)(x-5)-12/2(x+5)(x-5)-(x+1)(x-5)/2(x+5)(x-5)
=(2x+10-12-x ²+ 4x+5)/2(x ²- 25）
=(-x ²+ 6x+3)/(2x ²- 50)
=-(x ²- 6x-3)/(2x ²- 50)

### Calculate 1 + 1 + 2 / 1 + + 1 + 2 + 3 / 1 + 1 + 2 + 3 +... + 1 / 100=

Using the summation formula of arithmetic sequence, we know
1+2+3+4+.+n=（1+n）*N/2
Therefore, the original formula can be changed into 1 + 2 * (1 / (2 * 3) + 1 / (3 * 4) +. + 1 / (100 * 101))
By the split term method, 1 / (n (n + 1)) = (1 / N) - (1 / (n + 1))
Available
=1+2*（1/2-1/101）
=200/101

### X ^ 2-4 2x-2-x 1 + X + 2 3

Original formula = 2x / (x ^ 2-4) - 1 / (2-x) + 3 / (x + 2)
=2x/(x-2)(x+2)+1/(x-2)+3/(x+2)
=[2x+(x+2)+3(x-2)]/(x-2)(x+2)
=(6x-4)/(x-2)(x+2)
=2(3x-2)/(x-2)(x+2)

### 1. Calculation ① (x-1-x + 8 / 1) × X + 1 / 3; ② X + 3Y / X-Y ÷ x ²+ 6xy+9y ² Percent x ²- y ²- X + 2Y / Y; ③ (x-x + 2x / 1) ÷ x ²- 1 / 1 x ²- 2x+1 ④（x ²- 2X / x + 2-x ²- 4X + 1 / 4) ÷ x ³- 2x ² X-4 / 2

① (x-1-x + 8 / 1) × X + 1 / 3;
=（x ²- 1-8）/(x+1) × (x+1)/(x+3)
=x-3;
② X + 3Y / X-Y ÷ x ²+ 6xy+9y ² Percent x ²- y ²- X + 2Y / Y;
=(x-y)/(x+3y) × (x+3y) ²/ (x+y)(x-y)-2y/(x+y)
=(x+3y)/(x+y)-2y/(x+y)
=1;
③ (x-x + 2x / 1) ÷ x ²- 1 / 1 x ²- 2x+1
=(x ²+ x-2x)/(x+1) × (x+1)(x-1)/(x-1) ²
=x(x-1)/(x-1)
=x;