\(=\left[x^2\left(x-2\right)-2x\left(x-2\right)+3\left(x-2\right)\right]:\left(x-2\right)=\left[\left(x-2\right)\left(x^2-2x+3\right)\right]:\left(x-2\right)=x^2-2x+3\)
Rút gọn phân thức \(\frac{x^3-7x-6}{x^2\left(x-3\right)^2+4x\left(x-3\right)^2+4\left(x-3\right)^2}\)
6,Thực hiện phép tính
1,\(\frac{2a^3-2b^3}{3a+3b}.\frac{6a+6b}{a^2-2ab+b^2}\)
2,\(\frac{a^2+ab}{b-a}:\frac{a+b}{2a^2-2b^2}\)
3,\(\frac{x+y}{y-x}:\frac{x^2+xy}{3x^2-3y^2}\)
4,\(\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}\)
5,\(\frac{5x-15}{4x+4}:\frac{x^2-9}{x^2+2x+1}\)
6,\(\frac{6x+48}{7x-7}:\frac{x^2-64}{x^2-2x+1}\)
Giải các phương trình sau:
a) 1/x-2 - 1/x2 - 4 = 4/5
b) 1/x+2 + 1/(x+2)2 = 22
c) 3/2x-16 + 3x-20/x-8 + 1/8 = 13x-10x2/3x-24
d) 2 + 2x-8x/2x2+8x + 2x2+7x+23/2x2+7x-4 = 2x+5/2x-1
e) 1/2-x + 14/x2-9 = x-4/x+3 + 7/3+x
g) 3/2x+1 = 6/2x+3 + 8/4x2+8x+3
Thực hiện phép tính :
a) \(\frac{3x-2}{2xy}\)-\(\frac{7x-4}{2xy}\)
b) \(\frac{6}{x^2+4x}+\frac{3}{2x+8}\)
c) \(\frac{8xy}{3x-1}:\frac{12xy^3}{5-15x}\)
d) \(\frac{x^2}{x^2-4x+4}\) . \(\frac{2x-4}{4x}\)
a ) 5x ( 2 - 3x ) = 4 - 6x
b ) ( 5 - x ) ( 2 + 3x ) = 4 - 9x2
c ) 25 – x2 = 4x ( 5 + x )
d ) x2 - 2x + 1 = 3x ( x - 1 )
e ) 4 ( 7x - 3 ) = 7x2 - 3x
g ) ( x - 5 )4 + ( x - 3 )4 = 16 .
P = \(\dfrac{x^3-4x^2-x+4}{x^3-7x^2+14x-8}\)
Tìm x nguyên để P nguyên
bài tập 1: giải các phương trình sau:
a, \(\dfrac{3}{1-4x}\)= \(\dfrac{2}{4x+1}\)- \(\dfrac{8+6x}{16x^2-1}\)
b, \(\dfrac{3}{5x-1}\)+\(\dfrac{2}{3-5x}\)=\(\dfrac{4}{\left(1-5x\right)\left(5x-3\right)}\)
c, \(\dfrac{x+2}{x+1}\)+\(\dfrac{3}{x-2}\)=\(\dfrac{3}{x^2-x-2}+1\)
d, \(\dfrac{5-x}{4x^2-8x}+\dfrac{7}{8}=\dfrac{x-1}{2x\left(x-2\right)}+\dfrac{1}{8x-16}\)
e, \(\dfrac{x+6}{x+5}+\dfrac{x-5}{x+6}=\dfrac{2x^2+23x+61}{x^2+x-30}\)
f, \(\dfrac{x^2-x}{x+3}-\dfrac{x^2}{x-3}=\dfrac{7x^2-3x}{9-x^2}\)
Câu 3: Giải các phương trình sau bằng cách đưa về dạng ax+b=0
1. a, \(\frac{5x-2}{3}=\frac{5-3x}{2}\); b, \(\frac{10x+3}{12}=1+\frac{6+8x}{9}\)
c, \(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\); d, \(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)
e, \(\frac{7x-1}{6}+2x=\frac{16-x}{5}\); f, 4 (0,5-1,5x)=\(\frac{5x-6}{3}\)
g, \(\frac{3x+2}{2}-\frac{3x+1}{6}=\frac{5}{3}+2x\); h, \(\frac{x+4}{5}.x+4=\frac{x}{3}-\frac{x-2}{2}\)
i, \(\frac{4x+3}{5}-\frac{6x-2}{7}=\frac{5x+4}{3}+3\); k, \(\frac{5x+2}{6}-\frac{8x-1}{3}=\frac{4x+2}{5}-5\)
m, \(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{15}\); n, \(\frac{1}{4}\left(x+3\right)=3-\frac{1}{2}\left(x+1\right).\frac{1}{3}\left(x+2\right)\)
p, \(\frac{x}{3}-\frac{2x+1}{6}=\frac{x}{6}-x\); q, \(\frac{2+x}{5}-0,5x=\frac{1-2x}{4}+0,25\)
r, \(\frac{3x-11}{11}-\frac{x}{3}=\frac{3x-5}{7}-\frac{5x-3}{9}\); s, \(\frac{9x-0,7}{4}-\frac{5x-1,5}{7}=\frac{7x-1,1}{6}-\frac{5\left(0,4-2x\right)}{6}\)
t, \(\frac{2x-8}{6}.\frac{3x+1}{4}=\frac{9x-2}{8}+\frac{3x-1}{12}\); u, \(\frac{x+5}{4}-\frac{2x-3}{3}=\frac{6x-1}{3}+\frac{2x-1}{12}\)
v, \(\frac{5x-1}{10}+\frac{2x+3}{6}=\frac{x-8}{15}-\frac{x}{30}\); w, \(\frac{2x-\frac{4-3x}{5}}{15}=\frac{7x\frac{x-3}{2}}{5}-x+1\)
1) Phân tích các đa thức sau thành nhân tử:
a. \(^{3x^2-3y^2}\) c. \(x^2-3x+2\)
b. \(x^2-xy+7x-7y\) d. \(x^3+2x^2+xy^2-16x\)
2) Thực hiện các phép tính sau:
a. \(\dfrac{2x+6}{3x^2-x}:\dfrac{x^2+3x}{1-3x}\) b. \(\dfrac{x^2+4x-3}{x^3+1}-\dfrac{x-1}{x^2-x+1}+\dfrac{2}{x+1}\)
