The square of X + 8x + the square of 16 / 16-x △ 2x + 8 / 16 x-4 × x + 2 / 16 X-2 (A's square-2a / A + 2-A's square-4a + 4 / A-1) / / 4 / A The square of X-1 / x + 2x + 1 △ the square of X-1 / x + 1 - x + 1 Decompose the square of factor 8a-32-16a + 9b-2x-3x

The square of X + 8x + the square of 16 / 16-x △ 2x + 8 / 16 x-4 × x + 2 / 16 X-2 (A's square-2a / A + 2-A's square-4a + 4 / A-1) / / 4 / A The square of X-1 / x + 2x + 1 △ the square of X-1 / x + 1 - x + 1 Decompose the square of factor 8a-32-16a + 9b-2x-3x

1. Original formula = [(4 + x) (4-x) / (x + 4) ^ 2] / [(x-4) / 2 (x + 4)] × [(X-2) / (x + 2)] = 2 (2-x) / (x + 2); 2. Original formula = [(a + 2) / a (A-2) - (A-1) / (A-2) ^ 2] / (4-A) / a = - 1 / (A-2) ^ 2; 3. Original formula = [(x + 1) ^ 2 / (x + 1) (x-1)] / [(x + 1) / X (x-1)] - x + 1 = x-x + 1 = 1; 4, 8A ^ 2-32

The square of (2x + 1) (x-1) - (x-3) - x (2x-3), where x square - 8x-5 = 0, is evaluated after simplification

(2x+1)(x-1)-(x-3)²-x(2x-3)
=2x²-x-1-(x²-6x+9)-2x²+3x
=-x²+8x-10
=-(x²-8x)-10
=-15

In △ ABC, ab = AC = 12cm, BC = 6cm, D is the midpoint of BC, and the moving point P starts from point B and moves along the direction of B → a → C at the speed of 1cm per second. Suppose the moving time is t, then when t=______ The line passing through D and P divides the perimeter of △ ABC into two parts, one of which is twice as large as the other

There are two cases: (1) when point P is on AB, as shown in the figure, ∵ AB = AC = 12cm, BD = CD = 12bc = 12 × 6 = 3cm, let point P move for T seconds, then BP = t, AP = 12-t, from the meaning of the question: BP + BD = 12 (AP + AC + CD) or 12 (BP + BD) = AP + AC + CD, ∵ T + 3 = 12 (12-t + 12 + 3) or 12 (T + 3) = 12-t + 1

axial symmetry
In an alley with width AB = a, the length of a ladder is B, and the foot position of the ladder is p. when the top of the ladder is placed on one wall, the height from Q to the ground is C, and the angle between the ladder and the ground is 45 degrees. When the top of the ladder is placed on another wall, the height from the ground is D, and the angle between the ladder and the ground is 75 degrees
But why is RB perpendicular to PQ

Straight lines a and B are parallel, and the distance is three. Straight line C is perpendicular to a and B, and C intersects with a and B at points o and m respectively. There is a point P on the left part above straight line C. first, make the symmetric point P1 of P about a, and then make the symmetric point P2 of P1 about B, and find the length of p1p2?

6

On the problem of "axisymmetry"
In the following statements, the correct ones are ()
1) Two axisymmetric line segments must be on both sides of the axis of symmetry
2) The two sides of the angle are symmetrical about the line where the bisector of the angle lies
3) Two congruent triangles are symmetrical about a line
4) An equilateral triangle is an axisymmetric figure with three axes of symmetry
A 1, B 2, C 3, D 4

C
Three is wrong

If the coordinate of point P is (- A, 0), where 0 ＜ a ＜ 3, the line L is at x = 3 and parallel to the Y axis. The symmetric point of point P about the Y axis is P1, and the symmetric point of point P1 about the line L is P2. Find the length from P to P2

Because point P1 is the symmetric point of P about the Y axis, the distance from P to P1 is 2A. Because p1p2 is symmetric about the L axis, the distance is 2 (3-A), so the distance is the sum of the two, and we get 6

Given the symmetric point of point a (m-1,3) and point B (2, N + 1) with respect to the origin, then the coordinate of point P (m, n) with respect to the y-axis symmetry is?

Symmetric points of point a (m-1,3) and point B (2, N + 1) about the origin
m-1+2=0
n+1+3=0
m=-1,n=-4
The coordinates of point P (m, n) about y axis symmetry are (1, - 4)

Given that point P (x + y, x) and point m (5, y) are symmetric with respect to the Y axis, the coordinates of point P are obtained

Point P (x + y, x) and point m (5, y) are symmetric about the Y axis
Then:
x+y=-5
x=y
The solution is as follows
x=y=-5/2
Then the coordinates of point P are (- 5, - 5 / 2)

Given m (- 2.5, 1.5), n (2, - 1), find: (1) the coordinates of the point m about the x-axis symmetry; (2) the coordinates of the point n about the y-axis symmetry; (3) the coordinates of the two ends of the line Mn about the x-axis symmetry

(1) ∵ m (- 2.5, 1.5); (2) ∵ n (2, - 1); (3) M '(- 2.5, - 1.5); ∵ n (2, - 1); (2,1); (2,1); (2,1); (3) M' (- 2.5, - 1.5); ∵ n (2, - 1); (2,1); (2,1); (2,1); (2,1)