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.
Những câu hỏi liên quan
Rút gọn:
a) \(\frac{x^2+2x+1}{5x^3+5x^2}\)
b) \(\frac{10xy^2.\left(x+y\right)}{15xy.\left(x+y\right)^3}\)
c) \(\frac{2x^2+2x}{x^2+2x+1}\)
Giải từng bước giúp mình nhé. Thanks nhiều ạ!
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
\(\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)= \(\frac{2y}{3\left(x+y\right)^2}\)
\(\frac{x^2+2x+1}{5x^3+5x^2}=\frac{\left(x+1\right)^2}{5x^2\left(x+1\right)}=\frac{x+1}{5x^2}\)
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giúp mình rút gọn phân thức
\(\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)
\(\frac{x^2-xy-x+y}{x^2+xy-x-y}\)
\(\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)
\(=\frac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)\left(x+y\right)^2}\)
\(=\frac{10y}{15\left(x+y\right)^2}\)
\(\frac{x^2-xy-x+y}{x^2+xy-x-y}\)
\(=\frac{\left(x^2-x\right)-\left(xy-y\right)}{\left(x^2-x\right)+\left(xy-y\right)}\)
\(=\frac{x\left(x-1\right)-y\left(x-1\right)}{x\left(x-1\right)+y\left(x-1\right)}\)
\(=\frac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}\)
\(=\frac{x-y}{x+y}\)
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a)\(\frac{2xy}{3\left(x+y\right)^2}\)
b)=\(\frac{\left(x^2-xy\right)-\left(x-y\right)}{\left(x^2+xy\right)-\left(x+y\right)}\)=\(\frac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}\)
=\(\frac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}\)=\(\frac{\left(x-y\right)}{\left(x+y\right)}\)
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câu a của công chúa xinh xắn còn thiếu nha
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Rút gọn các viểu thức sau:
a) \(P=\left(5x-1\right)+2\left(1-5x\right)\left(4+5x\right)+\left(5x+4\right)^2\)
b) \(Q=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)
Làm giúp mình nhé!
a)P=2(1-5x)(4+5x)+(5x+4)2
=5x-1-50x2-30x+8+25x2+40x+16
=(-50x2+25x2)+(5x-30x+40x)+8+16-1
=-25x2+15x+23
b)Q=(x-y)3+(y+x)3+(y-x)3-3xy(x+y)
=(x+y)3-3xy(x+y)
=x3+y3
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Cho đề hept{begin{cases}2y^2-x^212left(x^3-yright)y^3-xend{cases}Leftrightarrow}hept{begin{cases}2left(y^2+1right)-left(x^2+1right)2xleft(2x^2+1right)-yleft(y^2+2right)0end{cases}}đặt ay^2+1,bx^2+1Leftrightarrowhept{begin{cases}2a-b2xleft(2b-1right)-yleft(a+1right)0end{cases}Leftrightarrowhept{begin{cases}b2a-2xleft(4a-5right)-ya-y0end{cases}}}Leftrightarrowhept{begin{cases}b2a-2afrac{5x+y}{4x-y}end{cases}Leftrightarrowhept{begin{cases}bfrac{2x+4y}{4x-y}afrac{5x+y}{4x-y}end{cases}}}Rightarrowhep...
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Cho đề \(\hept{\begin{cases}2y^2-x^2=1\\2\left(x^3-y\right)=y^3-x\end{cases}\Leftrightarrow}\)\(\hept{\begin{cases}2\left(y^2+1\right)-\left(x^2+1\right)=2\\x\left(2x^2+1\right)-y\left(y^2+2\right)=0\end{cases}}\)
đặt \(a=y^2+1,b=x^2+1\)
\(\Leftrightarrow\hept{\begin{cases}2a-b=2\\x\left(2b-1\right)-y\left(a+1\right)=0\end{cases}\Leftrightarrow\hept{\begin{cases}b=2a-2\\x\left(4a-5\right)-ya-y=0\end{cases}}}\Leftrightarrow\hept{\begin{cases}b=2a-2\\a=\frac{5x+y}{4x-y}\end{cases}\Leftrightarrow\hept{\begin{cases}b=\frac{2x+4y}{4x-y}\\a=\frac{5x+y}{4x-y}\end{cases}}}\)\(\Rightarrow\hept{\begin{cases}y^2+1=\frac{5x+y}{4x-y}\left(1\right)\\x^2+1=\frac{2x+4y}{4x-y}\left(2\right)\end{cases}}\)
pt(1)-pt(2),ta dc:\(\left(x-y\right)\left(\frac{3}{4x-y}+x+y\right)=0\)\(\Leftrightarrow\orbr{\begin{cases}x=y\left(3\right)\\\frac{3}{4x-y}+x+y=0\left(4\right)\end{cases}}\)
CM:PT (4) vô nghiệm giúp mình nha!Và xem lại nếu mình có lm sai hay thiếu đk j đó hãy chỉ giúp mình nha!!!Hoặc pt(4) có nghiệm thì hãy giải giúp mình luôn nha!Thanks
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) \(=\dfrac{36\left(x-2\right)^3}{-16\left(x-2\right)}=-9\left(x-2\right)^2=-9x^2+36x-36\)
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GIÚP MÌNH VỚI!Rút gọn phân thức:a) frac{2x+2y+5x+5y}{2x+2y-5x-5y}b) frac{15xleft(x+yright)^3}{5yleft(x+yright)^2}c) frac{5left(x-yright)-3left(y-xright)}{10left(x-yright)}d) frac{3left(x-yright)left(x-zright)^2}{6left(x-yright)left(x-zright)}h) frac{3xleft(1-xright)}{2left(x-1right)}j) frac{6x^2y^2}{8xy^5}
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GIÚP MÌNH VỚI!
Rút gọn phân thức:
a) \(\frac{2x+2y+5x+5y}{2x+2y-5x-5y}\)
b) \(\frac{15x\left(x+y\right)^3}{5y\left(x+y\right)^2}\)
c) \(\frac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}\)
d) \(\frac{3\left(x-y\right)\left(x-z\right)^2}{6\left(x-y\right)\left(x-z\right)}\)
h) \(\frac{3x\left(1-x\right)}{2\left(x-1\right)}\)
j) \(\frac{6x^2y^2}{8xy^5}\)
a) \(=\frac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}\)
\(=\frac{7\left(x+y\right)}{-3\left(x+y\right)}=\frac{-7}{3}\)
b)\(=\frac{3x\left(x+y\right)}{y}\)
c) \(\frac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}\)
\(=\frac{8\left(x-y\right)}{10\left(x-y\right)}=\frac{4}{5}\)
a) \(\frac{2x+2y+5x+5y}{2x+2y-5x-5y}=\frac{7x+7y}{-3x-3y}=\frac{7\left(x+y\right)}{-3\left(x+y\right)}=-\frac{7}{3}.\)
b) \(\frac{15x\left(x+y\right)^3}{5y\left(x+y\right)^2}=\frac{3x\left(x+y\right)}{y}=\frac{3x^2+3xy}{y}\)
c) \(\frac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\frac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}=\frac{8\left(x-y\right)}{10\left(x-y\right)}=\frac{4}{5}\)
d) \(\frac{3\left(x-y\right)\left(x-z\right)^2}{6\left(x-y\right)\left(x-z\right)}=\frac{x-z}{2}\)
h) \(\frac{3x\left(1-x\right)}{2\left(x-1\right)}=-\frac{3x\left(x-1\right)}{2\left(x-1\right)}=\frac{-3x}{2}\)
j) \(\frac{6x^2y^2}{8xy^5}=\frac{3x}{4y^3}\)
Câu b) bạn xem lại nhé.
Học tốt ^3^
14 tháng 2 2020 lúc 16:00
Bài 1: rút gọn phân thứca) frac{14xy^2left(2x-3yright)}{21x^2yleft(2x-3yright)^2}b) frac{8xyleft(3x-1right)^2}{12x^3left(1-3xright)}c) frac{20x^2-45}{left(2x+3right)^2}d) frac{5x^2-10xy}{2left(2y-xright)^3}e) frac{80x^3-125x}{3left(x-3right)-left(x-3right)left(8-4xright)}f) frac{9-left(x+5right)^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 saua) 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...
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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: \(a,\frac{7x-1}{2x^2+6x}=\frac{7x-1}{2x\left(x+3\right)}=\frac{\left(7x-1\right)\left(x-3\right)}{2x\left(x+3\right)\left(x-3\right)}\)
\(\frac{5-3x}{x^2-9}=\frac{5-3x}{\left(x-3\right)\left(x+3\right)}=\frac{\left(5-3x\right)2x}{2x\left(x-3\right)\left(x+3\right)}\)
\(b,\frac{x+1}{x-x^2}=\frac{x+1}{x\left(1-x\right)}=-\frac{x+1}{x\left(x+1\right)}=-\frac{2\left(x-1\right)\left(x+1\right)}{2x\left(x-1\right)^2}\)
\(\frac{x+2}{2-4x+2x^2}=\frac{x+2}{2\left(x-1\right)^2}=\frac{2x\left(x+2\right)}{2x\left(x-1\right)^2}\)
\(c,\frac{4x^2-3x+5}{x^3-1}=\frac{4x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\frac{2x}{x^2+x+1}=\frac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\frac{6}{x-1}=\frac{6\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(d,\frac{7}{5x}=\frac{7.2\left(2y-x\right)\left(2y+x\right)}{2.5x\left(2y-x\right)\left(2y+x\right)}\)
\(\frac{4}{x-2y}=-\frac{4}{2y-x}=-\frac{4.2.5x\left(2x+x\right)}{2.5x\left(2y-x\right)\left(2y+x\right)}\)
\(\frac{x-y}{8y^2-2x^2}=\frac{x-y}{2\left(4y^2-x^2\right)}=\frac{x-y}{2\left(2y-x\right)\left(2y+x\right)}=\frac{5x\left(x-y\right)}{2.5x.\left(2y-x\right)\left(2y+x\right)}\)
Rút gọn các phân thức sau
a,\(\frac{2x+2y+5x+5y}{2x+2y-5x-5y}\left(x\ne-y\right)\)
b,\(\frac{4x^2-4xy}{5x^3-5x^2y}\left(x\ne0,x\ne y\right)\)
ai làm đc 3 tick
ko ghi đề bài nha làm luôn
a) \(\frac{\left(2x+2y\right)+\left(5x+5y\right)}{\left(2x+2y\right)-\left(5x+5y\right)}=\frac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}=\frac{\left(2+5\right)\left(x+y\right)}{\left(2-5\right)\left(x+y\right)}=\frac{-7}{3}\)
b)\(\frac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\frac{4x}{5x^2}=\frac{4}{5x}\)
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a)ĐK: \(x\ne-y;x,y\ne0\)
\(\frac{2x+2y+5x+5y}{2x+2y-5x-5y}=\frac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}\)
\(=\frac{\left(x+y\right)\left(2+5\right)}{\left(x+y\right)\left(2-5\right)}=-\frac{7}{3}\)
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b) ĐK: ...bạn tự xét...
\(\frac{4x^2-4xy}{5x^3-5x^2y}=\frac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\frac{4x}{5x^2}=\frac{4}{5x}\)
Vậy ...
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