Rút gọn phân thức:
\(\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\) \(\frac{7x^2+14x+7}{3x^2+3x}\)
giúp mình rút gọn phân thức
\(\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)
\(\frac{x^2-xy-x+y}{x^2+xy-x-y}\)
\(\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)
\(=\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)\left(x+y\right)^2}\)
\(=\frac{10y}{15\left(x+y\right)^2}\)
\(\frac{x^2-xy-x+y}{x^2+xy-x-y}\)
\(=\frac{\left(x^2-x\right)-\left(xy-y\right)}{\left(x^2-x\right)+\left(xy-y\right)}\)
\(=\frac{x\left(x-1\right)-y\left(x-1\right)}{x\left(x-1\right)+y\left(x-1\right)}\)
\(=\frac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}\)
\(=\frac{x-y}{x+y}\)
a)\(\frac{2xy}{3\left(x+y\right)^2}\)
b)=\(\frac{\left(x^2-xy\right)-\left(x-y\right)}{\left(x^2+xy\right)-\left(x+y\right)}\)=\(\frac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}\)
=\(\frac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}\)=\(\frac{\left(x-y\right)}{\left(x+y\right)}\)
câu a của công chúa xinh xắn còn thiếu nha
Rút gọn phân thức:
\(\frac{x^2+2x+1}{5x^3+5x^2}\) \(\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)
Ta có
\(\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)= \(\frac{2y}{3\left(x+y\right)^2}\)
\(\frac{x^2+2x+1}{5x^3+5x^2}=\frac{\left(x+1\right)^2}{5x^2\left(x+1\right)}=\frac{x+1}{5x^2}\)
Rút gọn phân thức
\(\frac{5x^2+10xy+5y^2}{3x^3+3y^3}\)
\(\frac{-15x\left(x-y\right)}{3\left(y-x\right)}\)
\(\frac{5x^2+10xy+5y^2}{3x^3+3y^3}=\frac{5\left(x^2+2xy+y^2\right)}{3\left(x^3+y^3\right)}=\frac{5\left(x+y\right)^2}{3\left(x+y\right)\left(x^2-xy+y^2\right)}=\frac{5\left(x+y\right)}{3\left(x^2-xy+y^2\right)}\)
\(\frac{-15x\left(x-y\right)}{3\left(y-x\right)}=\frac{15x\left(y-x\right)}{3\left(y-x\right)}=\frac{15x}{3}\)
Rút gọn các phân thức sau:
a) \(\dfrac{6x^2y^2}{8xy^{ }5}\)
b) \(\dfrac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)
c) \(\dfrac{2x^2+2x
}{x+1}\)
d) \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)
e) \(\dfrac{36\left(x-2\right)^3}{32-16x}\)
a) \(\dfrac{6x^2y^2}{8xy^5}=\dfrac{3x}{4y^3}\)
b) \(=\dfrac{2y}{3\left(x+y\right)^2}=\dfrac{2y}{3x^2+6xy+3y^2}\)
c) \(=\dfrac{2x\left(x+1\right)}{x+1}=2x\)
d) \(=\dfrac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}=\dfrac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}=\dfrac{x-y}{x+y}\)
e) \(=\dfrac{36\left(x-2\right)^3}{-16\left(x-2\right)}=-9\left(x-2\right)^2=-9x^2+36x-36\)
rút gọn các phân thức:
a,\(\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)b,\(\frac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\)c,\(\frac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}\)
AD phân tích đa thức thành nhân tử ở tử thức và mẫu thức của từng phân thức
Rút gọn phân thức:
\(\frac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\)
\(\frac{\left(x-y\right)^3+3xy\left(x+y\right)+y^3}{x-6y}\)
\(\frac{x^2+y^2+z^2-2xy+2xz-2yz}{x^2-2xy+y^2-z^2}\)
c) hang dang thuc ( x -y+z)^2
o duoi phan h hang dang thuc luon
a) phan h nhan tu ra sao cho co tử la (x-1)(3x^2 -4x +1)
mau la (x-1)(2x^2 -x-3)
b ) k nhin dc de
\(\frac{\left(x-y\right)^3+3xy.\left(x+y\right)+y^3}{x-6y}\)
\(=\frac{x^3-3x^2y+3xy^2-y^3+3x^2y+3xy^2+y^3}{x-6y}\)
\(=\frac{x^3+\left(-3x^2y+3x^2y\right)+\left(3xy^2+3xy^2\right)+\left(-y^3+y^3\right)}{x-6y}\)
\(=\frac{x^3+6xy^2}{x-6y}\)
\(\frac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\)
\(=\frac{3x^3-3x^2-4x^2+4x+x-1}{2x^3-2x^2+x^2-x-3x+3}\)
\(=\frac{3x^2.\left(x-1\right)-4x.\left(x-1\right)+\left(x-1\right)}{2x^2.\left(x-1\right)+x.\left(x-1\right)-3.\left(x-1\right)}\)
\(=\frac{\left(x-1\right).\left(3x^2-4x+1\right)}{\left(x-1\right).\left(2x^2+x-3\right)}\)
\(=\frac{3x^2-3x-x+1}{2x^2-2x+3x-3}\)
\(=\frac{3x.\left(x-1\right)-\left(x-1\right)}{2x.\left(x-1\right)+3.\left(x-1\right)}\)
\(=\frac{\left(x-1\right).\left(3x-1\right)}{\left(x-1\right).\left(2x+3\right)}\)
\(=\frac{3x-1}{2x+3}\)
Rút gọn
a))\(\frac{x^2+2x+1}{5x^3+5x^2}\)
b)) \(\frac{10xy^2.\left(x+y\right)}{15xy.\left(x+y\right)^3}\)
Bạn nào biết làm giúp mình nhé! Thanks nhiều.
a)\(\frac{\left(x+1\right)^2}{5x^2\left(x+1\right)}\)=\(\frac{x+1}{5x^2}\)
b)\(\frac{10y}{15\left(x+y\right)^2}\)
Rút gọn phân thức ( giải chi tiết giúp e nha)
a: \(\frac{\left(2x-4\right).\left(x-3\right)}{\left(x-2\right).\left(3x^2-27\right)}\)
b: \(\frac{\left(2x^3+x^2-2x-1\right)}{x^3+2x^2-x-2}\)
c: \(\frac{3x^2-12x+12}{x⁴-8x}\)
d: \(\frac{7x^2+14+7}{3x^2+3x}\)
Mọi người cố gắng giúp e nha. E cảm ơn nhiều
Bài 1: rút gọn phân thức
a) \(\frac{14xy^2\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}\)
b) \(\frac{8xy\left(3x-1\right)^2}{12x^3\left(1-3x\right)}\)
c) \(\frac{20x^2-45}{\left(2x+3\right)^2}\)
d) \(\frac{5x^2-10xy}{2\left(2y-x\right)^3}\)
e) \(\frac{80x^3-125x}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\)
f) \(\frac{9-\left(x+5\right)^2}{x^2+4x+4}\)
g) \(\frac{32x-8x^2+2x^3}{x^3+64}\)
h) \(\frac{5x^3+5x}{x^4-1}\)
Bài 2: Quy đồng mẫu thức của các phân thức sau
a) \(\frac{7x-1}{2x^2+6x};\frac{5-3x}{x^2-9}\)
b) \(\frac{x+1}{x-x^2};\frac{x+2}{2-4x+2x^2}\)
c) \(\frac{4x^2-3x+5}{x^3-1};\frac{2x}{x^2+x+1};\frac{6}{x-1}\)
d) \(\frac{7}{5x};\frac{4}{x-2y};\frac{x-y}{8y^2-2x^2}\)
Bài 2: \(a,\frac{7x-1}{2x^2+6x}=\frac{7x-1}{2x\left(x+3\right)}=\frac{\left(7x-1\right)\left(x-3\right)}{2x\left(x+3\right)\left(x-3\right)}\)
\(\frac{5-3x}{x^2-9}=\frac{5-3x}{\left(x-3\right)\left(x+3\right)}=\frac{\left(5-3x\right)2x}{2x\left(x-3\right)\left(x+3\right)}\)
\(b,\frac{x+1}{x-x^2}=\frac{x+1}{x\left(1-x\right)}=-\frac{x+1}{x\left(x+1\right)}=-\frac{2\left(x-1\right)\left(x+1\right)}{2x\left(x-1\right)^2}\)
\(\frac{x+2}{2-4x+2x^2}=\frac{x+2}{2\left(x-1\right)^2}=\frac{2x\left(x+2\right)}{2x\left(x-1\right)^2}\)
\(c,\frac{4x^2-3x+5}{x^3-1}=\frac{4x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\frac{2x}{x^2+x+1}=\frac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\frac{6}{x-1}=\frac{6\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(d,\frac{7}{5x}=\frac{7.2\left(2y-x\right)\left(2y+x\right)}{2.5x\left(2y-x\right)\left(2y+x\right)}\)
\(\frac{4}{x-2y}=-\frac{4}{2y-x}=-\frac{4.2.5x\left(2x+x\right)}{2.5x\left(2y-x\right)\left(2y+x\right)}\)
\(\frac{x-y}{8y^2-2x^2}=\frac{x-y}{2\left(4y^2-x^2\right)}=\frac{x-y}{2\left(2y-x\right)\left(2y+x\right)}=\frac{5x\left(x-y\right)}{2.5x.\left(2y-x\right)\left(2y+x\right)}\)