\(1-3x-x^3+3x^2\)\(=\left(1-x^3\right)+\left(3x^2-3x\right)\)
\(=\left(1-x\right)\left(x^2+x+1\right)+3x\left(x-1\right)\)
\(=\left(x-1\right)\left(3x-x^2-x-1\right)=\left(x-1\right)\left(2x-x^2-1\right)\)
\(x^2-x-4y^2-2y\) phan tich da thuc thanh nhan tu
1.dùng định nghĩa hai pahn thức bằng nhau để CM phân thức sau bằng nhau
\(\dfrac{x^3-9x}{15-5x}=\dfrac{-x^2-3x}{5}\)
2.dung dinh nghia hai phan thuc bang nhau de tim A
\(\dfrac{4x^2-3x+7}{A}=\dfrac{4x-7}{2x+3}\)
tìm x sao cho gia tri bieu thuc \(\frac{3x-2}{4}\) khong nho ho gia tri bieu thuc\(\frac{3x+3}{6}\)
Rút gọn M và A sau đây :
M= \(\left(\dfrac{x}{x+3}+\dfrac{3-x}{x+3}.\dfrac{x^2+3x+9}{x^2-9}\right)\)
A= \(\left(\dfrac{3x}{1-3x}-\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
Bài 1:
i)\(\dfrac{x+1}{x-5}\)+\(\dfrac{x-18}{x-5}\)-\(\dfrac{x+2}{5-x}\)
j)\(\dfrac{3x\left(x-2\right)}{3x-2}\)+\(\dfrac{6x^2}{3x-2}\)-\(\dfrac{2\left(2-3x\right)}{2-3x}\)
n)\(\dfrac{2}{x}\)+\(\dfrac{3}{x-1}\)+\(\dfrac{1-4x}{x^2-x}\)
Bài 2:
j)\(\dfrac{2}{3x}\)-\(\dfrac{1}{2x-2}\)-\(\dfrac{x-4}{6x-6x^2}\)
Chủ đề 1: Thực hiện phép tính
1) (2x+3).(2x-3)-4x.(x+5)
2) 6/x2 - 9 + 5/x-3 + 1/x+3
3)5x.(x-3)+(x-2)2
4) 4x/x+2 - 3x/x-2 + 12x/ x2 - 4
5) x(x+2) - ( x-3)(x+3)
6) 1/3x-2 + -4/3+2 + 6-3x/9x2 - 4
7)2x.(3x-1)+(x+2)2
8) 6/x+3 - 6/x-3 + 9x+9/x2 - 9
9) (2x - 5)2 - x(4x-13)
10) x-1/x + 4/x+8 + 8/x2 + 8x
11) (2x+1)2 + (x-5)(x+5)-x(5x+7)
12) 6/x2-9 + 5/x-3 + 1/x+3
13) 6x(5x-2)+(2x+3)2
14) x/x-2 + -2/x-3 + x(1-x)/x2-9
15) (x-2)2-x(x+5)
16) 2/x+3 + 3/x-3 + -6/x2-9
17) 3x(x-3) + (3x-1)2
Rút gọn phân thức :
1 ) \(\frac{2x^3-x^2-2x+1}{x^3+3x^2-x-3}\)
2 ) \(\frac{x^2-3x+2}{x^3-3x^2+3x-1}\)
3) \(\frac{9x^2y^2+3x^2}{12xy^5+4xy^3}\)
1) rút gọn
a) \(\dfrac{x^2+3x-y^2-3y}{x^2-y^2}=\)
b) \(\dfrac{x^3+3x^2-2}{x^3+3x+4}=\)
giải phương trình
a.\(\left(2x-3\right)^2=\left(2x-3\right)\left(x+1\right)\)
b.\(x\left(2x-9\right)=3x\left(x-5\right)\)
c.\(3x-15=2x\left(x-5\right)\)
d.\(\dfrac{5-x}{2}=\dfrac{3x-4}{6}\)
e.\(\dfrac{3x+2}{2}-\dfrac{3x+1}{6}=2x+\dfrac{5}{3}\)