Cho \(\dfrac{15x}{7y^5}.\dfrac{2y^2}{x^6}=\dfrac{30}{7x^ay^b}\)
Tìm a b
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BT10: Thực hiện phép tính
\(a,\dfrac{4}{5}y^2x^5-x^3.x^2y^2\)
\(b,-xy^3-\dfrac{2}{7}y^2.xy\)
\(c,\dfrac{5}{6}xy^2z-\dfrac{1}{4}xyz.y\)
\(d,15x^4+7x^4-20x^2.x^2\)
\(e,\dfrac{1}{2}x^5y-\dfrac{3}{4}x^5y+xy.x^4\)
\(f,13x^2y^5-2x^2y^5+x^6\)
a: =-1/5x^5y^2
b: =-9/7xy^3
c: =7/12xy^2z
d: =2x^4
e: =3/4x^5y
f: =11x^2y^5+x^6
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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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Bài 1 : Tìm x,y,z biết :
a) 2x 3y ; 5y 7z và 3x - 7y + 5z -30
b) 3x 5y ; 7y 2z và x + y + z 74
c) x : z dfrac{2}{3} : dfrac{1}{2} ; z : y 1 : dfrac{4}{7} và y + z 66
d) x : y : z 3 : 4 : 5 và 2x^2 + 2y^2 - 3z^2 -100
e) x:y:z 2 : 5 : 6 và 2x^2 + 4y^2 - 4z^2 -324
f) dfrac{x-1}{2} dfrac{y-2}{3} dfrac{z-3}{4} và x-2y+3z14
g)dfrac{x-1}{2} dfrac{y+3}{4} dfrac{z-5}{6} và 5z-3x-4y50
h) dfrac{x}{2}dfrac{y}{7} và xy56
i)dfrac{x-y}{3}dfrac{x+y}{13}dfrac{xy}{200}
k) dfrac{x-5}{6}d...
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Bài 1 : Tìm x,y,z biết :
a) 2x = 3y ; 5y = 7z và 3x - 7y + 5z = -30
b) 3x =5y ; 7y = 2z và x + y + z = 74
c) x : z = \(\dfrac{2}{3}\) : \(\dfrac{1}{2}\) ; z : y = 1 : \(\dfrac{4}{7}\) và y + z = 66
d) x : y : z = 3 : 4 : 5 và \(2x^2\) + \(2y^2\) - \(3z^2\) = -100
e) \(x:y:z\) = 2 : 5 : 6 và \(2x^2\) + \(4y^2\) - \(4z^2\) = -324
f) \(\dfrac{x-1}{2}\) = \(\dfrac{y-2}{3}\) = \(\dfrac{z-3}{4}\) và \(x-2y+3z=14\)
g)\(\dfrac{x-1}{2}\) = \(\dfrac{y+3}{4}\) =\(\dfrac{z-5}{6}\) và \(5z-3x-4y=50\)
h) \(\dfrac{x}{2}=\dfrac{y}{7}\) và \(xy=56\)
i)\(\dfrac{x-y}{3}=\dfrac{x+y}{13}=\dfrac{xy}{200}\)
k) \(\dfrac{x-5}{6}=\dfrac{x+5}{18}\)
l) \(\dfrac{2x-11}{12}=\dfrac{x+5}{20}\)
Hãy làm các phép chia sau :
a) \(\dfrac{7x+2}{3xy^3}:\dfrac{14x+4}{x^2y}\)
b) \(\dfrac{8xy}{3x-1}:\dfrac{12xy^3}{5-15x}\)
c) \(\dfrac{27-x^3}{5x+5}:\dfrac{2x-6}{3x+3}\)
d) \(\left(4x^2-16\right):\dfrac{3x+6}{7x-2}\)
e) \(\dfrac{3x^3+3}{x-1}:\left(x^2-x+1\right)\)
1, Thực hiện phép tính:
a, dfrac{1-3x}{2}+dfrac{x+3}{2}
b, dfrac{2left(x+yright)left(x-yright)}{x}-dfrac{-2y^2}{x}
c, dfrac{3x+1}{x+y}-dfrac{2x-3}{x+y}
d, dfrac{xy}{2x-y}-dfrac{x^2-1}{y-2x}
e, dfrac{4x-1}{3x^2y}-dfrac{7x-1}{3x^2y}
2, Thực hiện phép tính:
a, dfrac{1}{x}.dfrac{6x}{y}
b, dfrac{2x^2}{y}.3xy^2
c, dfrac{15x}{7y^3}.dfrac{2y^2}{x^2}
d, dfrac{2x^2}{x-y}.dfrac{y}{5x^3}
e, dfrac{5x+10}{4x-8}.dfrac{4-2x}{x+2}
f, dfrac{x^2-36}{2x+10}.dfrac{3}{6-x}
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1, Thực hiện phép tính:
a, \(\dfrac{1-3x}{2}+\dfrac{x+3}{2}\)
b, \(\dfrac{2\left(x+y\right)\left(x-y\right)}{x}-\dfrac{-2y^2}{x}\)
c, \(\dfrac{3x+1}{x+y}-\dfrac{2x-3}{x+y}\)
d, \(\dfrac{xy}{2x-y}-\dfrac{x^2-1}{y-2x}\)
e, \(\dfrac{4x-1}{3x^2y}-\dfrac{7x-1}{3x^2y}\)
2, Thực hiện phép tính:
a, \(\dfrac{1}{x}.\dfrac{6x}{y}\)
b, \(\dfrac{2x^2}{y}.3xy^2\)
c, \(\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}\)
d, \(\dfrac{2x^2}{x-y}.\dfrac{y}{5x^3}\)
e, \(\dfrac{5x+10}{4x-8}.\dfrac{4-2x}{x+2}\)
f, \(\dfrac{x^2-36}{2x+10}.\dfrac{3}{6-x}\)
2)
a) \(\dfrac{1}{x}.\dfrac{6x}{y}\)
\(=\dfrac{6x}{xy}\)
\(=\dfrac{6}{y}\)
b) \(\dfrac{2x^2}{y}.3xy^2\)
\(=\dfrac{2x^2.3xy^2}{y}\)
\(=\dfrac{6x^3y^2}{y}\)
\(=6x^3y\)
c) \(\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}\)
\(=\dfrac{15x.2y^2}{7y^3.x^2}\)
\(=\dfrac{30xy^2}{7x^2y^3}\)
\(=\dfrac{30}{7xy}\)
d) \(\dfrac{2x^2}{x-y}.\dfrac{y}{5x^3}\)
\(=\dfrac{2x^2.y}{\left(x-y\right).5x^3}\)
\(=\dfrac{2y}{5x\left(x-y\right)}\)
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BT11: Tìm hiệu A-B biết
\(a,A-\dfrac{3}{8}xy^2-B+\dfrac{5}{6}x^2y=\dfrac{3}{4}x^2y-\dfrac{5}{8}xy^2\)
\(b,5xy^3-A-\dfrac{5}{8}yx^3+B=\dfrac{21}{4}xy^3-\dfrac{7}{6}x^3y\)
a/
\(\Leftrightarrow A=\dfrac{3}{8}xy^2+B-\dfrac{5}{6}x^2y+\dfrac{3}{4}x^2y-\dfrac{5}{8}xy^2\\ \Leftrightarrow A-B=-\dfrac{1}{12}x^2y-\dfrac{1}{4}xy^2\)
b/
\(\Leftrightarrow A-B=5xy^3-\dfrac{5}{8}yx^3-\dfrac{21}{4}xy^3+\dfrac{3}{7}x^3y\\ \Leftrightarrow A-B=-\dfrac{1}{4}xy^3-\dfrac{11}{56}x^3y\)
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Thực hiện các phép tính sau :
a) \(\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}\)
b) \(\dfrac{4y^2}{11x^4}.\left(-\dfrac{3x^2}{8y}\right)\)
c) \(\dfrac{x^3-8}{5x+20}.\dfrac{x^2+4x}{x^2+2x+4}\)
a) \(\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}=\dfrac{15x.2y^2}{7y^3.x^2}=\dfrac{30}{7xy}\)
b) \(\dfrac{4y^2}{11x^4}.\left(-\dfrac{3x^2}{8y}\right)=\dfrac{-4y^2.3x^2}{11x^4.8y}=\dfrac{-3y}{22x^2}\)
c) \(\dfrac{x^3-8}{5x+20}.\dfrac{x^2+4x}{x^2+2x+4}\\ =\dfrac{\left(x-2\right)\left(x^2+2x+4\right)}{5\left(x+4\right)}.\dfrac{x\left(x+4\right)}{x^2+2x+4}\\ =\dfrac{x^2-2x}{5}\)
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Câu 9: Thực hiện phép tính:
a) dfrac{3x-2}{2xy}+dfrac{7x+2}{2xy}.
b) dfrac{5x+y^2}{x^2y}+dfrac{x^2-5y}{xy^2}.
c) dfrac{3x-2}{2xy}-dfrac{7x-y}{2xy}.
d) dfrac{5x+y^2}{x^2y}-dfrac{5y-x^2}{xy^2}.
e) dfrac{16xy}{3x-1}.dfrac{3-9x}{12xy^3}.
f) dfrac{8xy}{3x-1}:dfrac{12xy^3}{5-15x}.
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Câu 9: Thực hiện phép tính:
a) \(\dfrac{3x-2}{2xy}+\dfrac{7x+2}{2xy}\).
b) \(\dfrac{5x+y^2}{x^2y}+\dfrac{x^2-5y}{xy^2}\).
c) \(\dfrac{3x-2}{2xy}-\dfrac{7x-y}{2xy}\).
d) \(\dfrac{5x+y^2}{x^2y}-\dfrac{5y-x^2}{xy^2}\).
e) \(\dfrac{16xy}{3x-1}.\dfrac{3-9x}{12xy^3}\).
f) \(\dfrac{8xy}{3x-1}:\dfrac{12xy^3}{5-15x}\).
a) \(\dfrac{3x-2}{2xy}+\dfrac{7x+2}{2xy}\)
\(=\dfrac{\left(3x-2\right)+\left(7x+2\right)}{2xy}\)
\(=\dfrac{3x-2+7x+2}{2xy}\)
\(=\dfrac{10x}{2xy}\)
\(=\dfrac{5}{y}\)
b) \(\dfrac{5x+y^2}{x^2y}+\dfrac{x^2-5y}{xy^2}\) MTC: \(x^2y^2\)
\(=\dfrac{y\left(5x+y^2\right)}{x^2y^2}+\dfrac{x\left(x^2-5y\right)}{x^2y^2}\)
\(=\dfrac{y\left(5x+y^2\right)+x\left(x^2-5y\right)}{x^2y^2}\)
\(=\dfrac{5xy+y^3+x^3-5xy}{x^2y^2}\)
\(=\dfrac{y^3+x^3}{x^2y^2}\)
c) \(\dfrac{3x-2}{2xy}-\dfrac{7x-y}{2xy}\)
\(=\dfrac{\left(3x-2\right)-\left(7x-y\right)}{2xy}\)
\(=\dfrac{3x-2-7x+y}{2xy}\)
\(=\dfrac{-2-4x+y}{2xy}\)
d) \(\dfrac{5x+y^2}{x^2y}-\dfrac{5y-x^2}{xy^2}\) MTC: \(x^2y^2\)
\(=\dfrac{y\left(5x+y^2\right)}{x^2y^2}-\dfrac{x\left(5y-x^2\right)}{x^2y^2}\)
\(=\dfrac{y\left(5x+y^2\right)-x\left(5y-x^2\right)}{x^2y^2}\)
\(=\dfrac{5xy+y^3-5xy+x^3}{x^2y^2}\)
\(=\dfrac{y^3+x^3}{x^2y^2}\)
e) \(\dfrac{16xy}{3x-1}.\dfrac{3-9x}{12xy^3}\)
\(=\dfrac{16xy\left(3-9x\right)}{12xy^3\left(3x-1\right)}\)
\(=\dfrac{4\left(3-9x\right)}{3y^2\left(3x-1\right)}\)
\(=\dfrac{-4\left(9x-3\right)}{3y^2\left(3x-1\right)}\)
\(=\dfrac{-4.3\left(3x-1\right)}{3y^2\left(3x-1\right)}\)
\(=\dfrac{-12}{3y^2}\)
\(=\dfrac{-4}{y^2}\)
f) \(\dfrac{8xy}{3x-1}:\dfrac{12xy^3}{5-15x}\)
\(=\dfrac{8xy}{3x-1}.\dfrac{5-15x}{12xy^3}\)
\(=\dfrac{8xy\left(5-15x\right)}{12xy^3\left(3x-1\right)}\)
\(=\dfrac{2\left(5-15x\right)}{3y^2\left(3x-1\right)}\)
\(=\dfrac{-2\left(15x-5\right)}{3y^2\left(3x-1\right)}\)
\(=\dfrac{-2.5\left(3x-1\right)}{3y^2\left(3x-1\right)}\)
\(=\dfrac{-10}{3y^2}\)
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1. Tìm x, y biết:
a. \(\dfrac{7x-3z}{5}=\dfrac{3y-5x}{7}=\dfrac{5z-7y}{3}\) và \(x+y+z=30\)
b. \(\dfrac{3x-4y}{2}=\dfrac{4x-2z}{3}=\dfrac{2y-3x}{4}\) và \(x-2y+3z=8\)
2. Một tam giác có độ dài ba cạnh tỉ lệ với 2,3,5. Hỏi chiều cao tương ứng với ba cạnh đó tỉ lệ với những số nào?
\(\dfrac{7x-3z}{5}=\dfrac{3y-5x}{7}=\dfrac{5z-7y}{3}\)
\(\Rightarrow\dfrac{35x-15z}{25}=\dfrac{21y-35x}{49}=\dfrac{15z-21y}{9}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{35x-15z}{25}=\dfrac{21y-35x}{49}=\dfrac{15z-21y}{9}\)
\(=\dfrac{35x-15z+21y-35x+15z-21y}{25+49+9}\)
\(=\dfrac{0}{25+49+9}=0\)
\(\Rightarrow\left\{{}\begin{matrix}7x=3z\Rightarrow\dfrac{x}{3}=\dfrac{z}{7}\\3y=5x\Rightarrow\dfrac{x}{3}=\dfrac{y}{5}\\5z=7y\Rightarrow\dfrac{z}{7}=\dfrac{y}{5}\end{matrix}\right.\)
\(\Rightarrow\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{7}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{x+y+z}{3+5+7}=\dfrac{30}{15}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.3=6\\y=2.5=10\\z=2.7=14\end{matrix}\right.\)
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