Tính\(\frac{2x-3y}{x+2y}\) \(\frac{2x-3y}{x+2y}\)\(\frac{2x-3y}{x+2y}\)
\(\dfrac{2x-3y}{x+2y}=\dfrac{2}{3}\)
Những câu hỏi liên quan
a,\(\dfrac{x+1}{x-3}+\dfrac{-2x^2+2x}{x^2-9}+\dfrac{x-1}{x+3}\)
b,\(\dfrac{1-2x}{6x^3y}+\dfrac{3+2y}{6x^3y}+\dfrac{2x-4}{6x^3y}\)
c,\(\dfrac{5}{2x^2y}+\dfrac{3}{5xy^2}+\dfrac{x}{3y^3}\)
d,\(\dfrac{5}{4\left(x+2\right)}+\dfrac{8-x}{4x^2+8x}\)
c,\(\dfrac{x^2+2}{x^3+1}+\dfrac{2}{x^2+x+1}+\dfrac{1}{1-x}\)
\(a,=\dfrac{x^2+4x+3-2x^2+2x+x^2-4x+3}{\left(x-3\right)\left(x+3\right)}=\dfrac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{2}{x-3}\\ b,=\dfrac{1-2x+3+2y+2x-4}{6x^3y}=\dfrac{2y}{6x^3y}=\dfrac{1}{x^2}\\ c,=\dfrac{75y^2+18xy+10x^2}{30x^2y^3}\\ d,=\dfrac{5x+8-x}{4x\left(x+2\right)}=\dfrac{4\left(x+2\right)}{4x\left(x+2\right)}=\dfrac{1}{x}\\ c,=\dfrac{x^2+2+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x^2+x+1}\)
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Cho x,y khác 0.
CMR : \(\frac{2x^2+3y^2}{2x^3+3y^3}+\frac{3x^2+2y^2}{3x^3+2y^3}\le\frac{4}{x+y}\)
Đề kì vậy bạn. Sao vế trái không có \(y\) vậy?
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\(\left\{{}\begin{matrix}\dfrac{2x-2y}{5}+\dfrac{5x-3y}{3}=x+1\\\dfrac{2x-3y}{3}+\dfrac{4x-3y}{2}=y+1\end{matrix}\right.\)
Tính
a)Cho \(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\)Tính \(\frac{x+2y-3z}{2x-3y+z}\)
b) Cho \(2x=3y=4z\)Tinh \(\frac{x+3y+5z}{3x-2y+4z}\)
BT11: Tìm hiệu A-B biếta,-x^2y+A+2xy^2-B3x^2y-4xy^2b,5xy^2-A-6yx^2+B-7xy^2+8x^2yc,3x^2y^3-A-5x^3y^2+B8x^2y^3-4x^3yd,-6x^2y^3+A-3x^3y^2-B2x^2y^3-7x^3ye,A-dfrac{3}{8}xy^2-B+dfrac{5}{6}x^2ydfrac{3}{4}x^2y-dfrac{5}{8}xy^2f,5xy^3-A-dfrac{5}{8}yx^3+Bdfrac{21}{4}xy^3-dfrac{7}{6}x^3y
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BT11: Tìm hiệu A-B biết
\(a,-x^2y+A+2xy^2-B=3x^2y-4xy^2\)
\(b,5xy^2-A-6yx^2+B=-7xy^2+8x^2y\)
\(c,3x^2y^3-A-5x^3y^2+B=8x^2y^3-4x^3y\)
\(d,-6x^2y^3+A-3x^3y^2-B=2x^2y^3-7x^3y\)
\(e,A-\dfrac{3}{8}xy^2-B+\dfrac{5}{6}x^2y=\dfrac{3}{4}x^2y-\dfrac{5}{8}xy^2\)
\(f,5xy^3-A-\dfrac{5}{8}yx^3+B=\dfrac{21}{4}xy^3-\dfrac{7}{6}x^3y\)
a: =>A-B=3x^2y-4xy^2+x^2y-2xy^2=4x^2y-6xy^2
b: =>B-A=-7xy^2+8x^2y-5xy^2+6x^2y=-12xy^2+14x^2y
=>A-B=12xy^2-14x^2y
c: =>B-A=8x^2y^3-4x^3y-3x^2y^3+5x^3y^2=5x^2y^3+x^3y^2
=>A-B=-5x^2y^3-x^3y^2
d: =>A-B=2x^2y^3-7x^3y+6x^2y^3+3x^3y^2=8x^2y^3-7x^3y+3x^3y^2
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RÚt gọn : \(\frac{2x+y}{2x+2y}-\frac{x+2y}{x-y}+\frac{5}{x}-\frac{4x}{3x^2-3y^2}\)
\(=\dfrac{2x+y}{2\left(x+y\right)}-\dfrac{x+2y}{x-y}+\dfrac{5}{x}-\dfrac{4x}{3\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{2x^2-2xy+xy-y^2}{2\left(x+y\right)\left(x-y\right)}-\dfrac{2\left(x+2y\right)\left(x-y\right)}{2\left(x-y\right)\left(x+y\right)}+\dfrac{5}{x}-\dfrac{4x}{3\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{2x^2-xy-y^2-2\left(x^2+xy-2y^2\right)}{2\left(x-y\right)\left(x+y\right)}-\dfrac{4x}{3\left(x-y\right)\left(x+y\right)}+\dfrac{5}{x}\)
\(=\dfrac{2x^2-xy-y^2-2x^2-2xy+4y^2}{2\left(x-y\right)\left(x+y\right)}-\dfrac{4x}{3\left(x-y\right)\left(x+y\right)}+\dfrac{5}{x}\)
\(=\dfrac{-3xy+3y^2}{2\left(x-y\right)\left(x+y\right)}-\dfrac{4x}{3\left(x-y\right)\left(x+y\right)}+\dfrac{5}{x}\)
\(=\dfrac{-9xy+9y^2-8x}{6\left(x-y\right)\left(x+y\right)}+\dfrac{5}{x}\)
\(=\dfrac{-9x^2y+9xy^2-8x^2+30\left(x^2-y^2\right)}{6x\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{-9x^2y+9xy^2+22x^2-30y^2}{6x\cdot\left(x-y\right)\left(x+y\right)}\)
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Thực hiện phép tính:a) ( 5x4 – 3x3 + x2 ):3x2 b) ( 5xy2 + 9xy – x2 y2) : ( -xy)c) (x^3y^3-dfrac{1}{2}x^2y^3-x^3y^2) :dfrac{1}{3}x^2y^2 d)left(x^3-2x^2y+3xy^2right):left(-dfrac{1}{2}xright) e) (30x4y3 - 20x2y3 + 6x4y4) : 5x2y3
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Thực hiện phép tính:
a) ( 5x4 – 3x3 + x2 ):3x2 b) ( 5xy2 + 9xy – x2 y2) : ( -xy)
c) (\(x^3y^3-\dfrac{1}{2}x^2y^3-x^3y^2\)) :\(\dfrac{1}{3}x^2y^2\) d)\(\left(x^3-2x^2y+3xy^2\right):\left(-\dfrac{1}{2}x\right)\)
e) (30x4y3 - 20x2y3 + 6x4y4) : 5x2y3
a: \(=\dfrac{5}{3}x^2-x+\dfrac{1}{3}\)
b: \(=-5y-9+xy\)
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Rút gọn biểu thức
A= \(1+\left[\frac{2x^3y^2+2x^2y^3}{x+y}:\left(\frac{2x^2y^2}{x^2+xy}+\frac{2x^2y^2}{y^2+xy}\right)\right]\)
a) (x - 2y)3
b) (2x + y)3
c) (\(\dfrac{1}{3}\)x - 1)3
d) (x + \(\dfrac{1}{3}\)y)3
e) (2x - 3y)3
f) (x2 - 2y)3
g) (\(\dfrac{1}{2}\)x - y)3
\(\)a: \(\left(x-2y\right)^3\)
\(=x^3-3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2-\left(2y\right)^3\)
\(=x^3-6x^2y+12xy^2-8y^3\)
b: \(\left(2x+y\right)^3=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2+y^3\)
\(=8x^3+12x^2y+6xy^2+y^3\)
c: \(\left(\dfrac{1}{3}x-1\right)^3=\left(\dfrac{1}{3}x\right)^3-3\cdot\left(\dfrac{1}{3}x\right)^2\cdot1+3\cdot\dfrac{1}{3}x\cdot1^2-1^3\)
\(=\dfrac{1}{27}x^3-\dfrac{1}{3}x^2+x-1\)
d: \(\left(x+\dfrac{1}{3}y\right)^3\)
\(=x^3+3\cdot x^2\cdot\dfrac{1}{3}y+3\cdot x\cdot\left(\dfrac{1}{3}y\right)^2+\left(\dfrac{1}{3}y\right)^3\)
\(=x^3+x^2y+\dfrac{1}{3}xy^2+\dfrac{1}{27}y^3\)
e: (2x-3y)3
\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot3y+3\cdot2x\cdot\left(3y\right)^2-\left(3y\right)^3\)
\(=8x^3-36x^2y+54xy^2-27y^3\)
f: \(\left(x^2-2y\right)^3\)
\(=\left(x^2\right)^3-3\cdot\left(x^2\right)^2\cdot2y+3\cdot x^2\cdot\left(2y\right)^2-\left(2y\right)^3\)
\(=x^6-6x^4y+12x^2y^2-8y^3\)
g: \(\left(\dfrac{1}{2}x-y\right)^3=\left(\dfrac{1}{2}x\right)^3-3\cdot\left(\dfrac{1}{2}x\right)^2\cdot y+3\cdot\dfrac{1}{2}x\cdot y^2-y^3\)
\(=\dfrac{1}{8}x^3-\dfrac{3}{4}x^2y+\dfrac{3}{2}xy^2-y^3\)
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