Các bạn giỏi Toán vào giúp mình cái:
Tìm giá trị biểu thức: \(P=\frac{3x+2y}{x-2y+4}\) biết\(\frac{2}{x-1}=\frac{3}{2y-3}\)

Thầy giải như sau: \(\frac{2}{x+1}=\frac{3}{2y-3}=\frac{6}{3x+3}=\frac{9}{3x+2y}\)(1)

Mặt khác:\(\frac{2}{x+1}=\frac{3}{2y-3}=\frac{-1}{x+1-2y+3}=\frac{-1}{x-2y+4}\)(2)

Từ (1) và (2) => \(\frac{9}{3x+2y}=\frac{-1}{x-2y+4}\)

=>\(\frac{9}{-1}=\frac{3x+2y}{x-2y+4}=-9\)

Vậy P = -9

Mình thắc mắc chỗ (2) đó các bạn, ở phần \(\frac{-1}{x+1-2y+3}\) đáng lẽ phải là \(\frac{-1}{x+1-2y-3}\) chứ

Giúp mình với

8,Thực hiện phép tính

a,\(\frac{5x^2-y^2}{xy}-\frac{3x-2y}{y}\)

b,\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)

c,\(\frac{2x}{x^2+2xy}+\frac{y}{xy-2y^2}+\frac{4}{x^2-4y^2}\) 

d,\(\frac{1}{x-y}+\frac{3xy}{y^3-x^3}+\frac{x-y}{x^2+xy+y^2}\) 

e,\(\frac{2x+y}{2x^2-xy}+\frac{16x}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}\) 

f,\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)

Thực hiện phép tính:

1,\(\frac{1-2x}{2x}+\frac{2x}{2x-1}+\frac{1}{2x-4x^2}\)

2,\(\frac{x^2+2}{x^3-1}+\frac{2}{x^2+x+1}+\frac{1}{1-x}\)

3,\(\frac{x}{x-2y}+\frac{x}{x+2y}+\frac{4xy}{4y^2-x^2}\)

4,\(\frac{2x}{x^2+2xy}+\frac{y}{xy-2y^2}+\frac{4}{x^2-4y^2}\)

5,\(\left(\frac{9}{x^3-9x}+\frac{1}{x+3}\right):\left(\frac{x-3}{x^2+3x}-\frac{x}{3x+9}\right)\)

Bài 1: Thu gọn

a) \(\frac{1}{5}x^4y^3-3x^4y^3\)

b) \(5x^2y^5-\frac{1}{4}x^2y^5\)

c) \(\frac{1}{7}x^2y^3.\left(-\frac{14}{3}xy^2\right)-\frac{1}{2}xy.\left(x^2y^{\text{4}}\right)\)

d) \(\left(3xy\right)^2.\left(-\frac{1}{2}x^3y^2\right)\)

e) \(-\frac{1}{4}xy^2+\frac{2}{5}x^2y+\frac{1}{2}xy^2-x^2y\)

f) \(\frac{1}{2}x^4y.\left(-\frac{2}{3}x^3y^2\right)-\frac{1}{3}x^7y^3\)

g) \(\frac{1}{2}x^2y.\left(-10x^3yz^2\right).\frac{1}{4}x^5y^3z\)

h) \(4.\left(-\frac{1}{2}x\right)^2-\frac{3}{2}x.\left(-x\right)+\frac{1}{3}x^2\)

i) \(1\frac{2}{3}x^3y.\left(\frac{-1}{2}xy^2\right)^2-\frac{5}{4}.\frac{8}{15}x^3y.\left(-\frac{1}{2}xy^2\right)^2\)

k) \(-\frac{3}{2}xy^2.\left(\frac{3}{4}x^2y\right)^2-\frac{3}{5}xy.\left(-\frac{1}{3}x^4y^3\right)+\left(-x^2y\right)^2.\left(xy\right)^2\)

n) \(-2\frac{1}{5}xy.\left(-5x\right)^2+\frac{3}{4}y.\frac{2}{3}\left(-x^3\right)-\frac{1}{9}.\left(-x\right)^3.\frac{1}{3}y\)

m) \(\left(-\frac{1}{3}xy^2\right)^2.\left(3x^2y\right)^3.\left(-\frac{5}{2}xy^2z^3\right)^{^2}\)

p) \(-2y.\left|2\right|x^4y^5.\left|-\frac{3}{4}\right|x^3y^2z\)

bài 1 : thực hiện các phép tính

a. \(\frac{4x-1}{3x^2y}-\frac{7x-1}{3x^2y}\)

b.\(\frac{4x+1}{2}-\frac{3x+2}{3}\)

c.\(\frac{5x^2-y^2}{xy}-\frac{3x-2y}{y}\)

d.\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)

e.\(\frac{x+3}{x}-\frac{x}{x-3}+\frac{9}{x^2-3x}\)

f.\(\frac{x+3}{x^2-1}-\frac{1}{x^2+x}\)

g.\(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{-10x+8}{9x^2-4}\)

h.\(\frac{x+9y}{x^2-9y^2}-\frac{3y}{x^2+3xy}\)

i.\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)

bài 1: Thực hiện các phép tính

a.\(\frac{4x-1}{3x^2y}-\frac{7x-2}{3x^2y}\)

b.\(\frac{4x+1}{2}-\frac{3x+2}{3}\)

c.\(\frac{5x^2-y^2}{xy}-\frac{3x-2y}{y}\)

d.\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)

e. \(\frac{x+3}{x}-\frac{x}{x-3}+\frac{9}{x^2-3x}\)

f..\(\frac{x+3}{x^2-1}-\frac{1}{x^2+x}\)

g. \(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{-10x+8}{9x^2-4}\)

h.\(\frac{x+9y}{x^2-9y^2}-\frac{3y}{x^2+3xy}\)

i.\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)