Bài 1:Tìm đa thức M
a)\(\dfrac{^{x^3}+27}{x^2-3x+9}\)=\(\dfrac{x+3}{M}\)
b)\(\dfrac{M}{x+4}\)=\(\dfrac{x^2-8x+16}{16-x^2}\)
c)\(\dfrac{x-2y}{M}\)=\(\dfrac{3x^2-7xy+2y^2}{3x^2+5xy-2y^2}\)
Những câu hỏi liên quan
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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tính:
a, \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
b, 2y - \(\dfrac{6xy+2y}{3x+2y}+\dfrac{2y-9x^2}{3x+2y}\)
Tính
a) \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
b) \(2y+\dfrac{6xy+2y}{3x+2y}+\dfrac{2y-9x^2}{3x+2y}\)
cho mik sửa lại câu
b) \(2y-\dfrac{6xy+2y}{3x+2y}+\dfrac{2y-9x^2}{3x+2y}\)
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b) \(2y-\dfrac{6xy+2y}{3x+2y}+\dfrac{2y-9x^2}{3x+2y}\)
\(=\dfrac{2y\left(3x+2y\right)}{3x+2y}-\dfrac{6xy+2y}{3x+2y}+\dfrac{2y-9x^2}{3x+2y}\)
\(=\dfrac{2y\left(3x+2y\right)-\left(6xy+2y\right)+\left(2y-9x^2\right)}{3x+2y}\)
\(=\dfrac{6xy+4y^2-6xy-2y+2y-9x^2}{3x+2y}\)
\(=\dfrac{4y^2-9x^2}{3x+2y}\)
\(=\dfrac{-\left(9x^2-4y^2\right)}{3x+2y}\)
\(=\dfrac{-\left[\left(3x\right)^2-\left(2y\right)^2\right]}{3x+2y}\)
\(=\dfrac{-\left(3x-2y\right)\left(3x+2y\right)}{3x+2y}\)
\(=-\left(3x-2y\right)\)
\(=-3x+2y\)
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a)\(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{1+x}{\left(1-x\right)\left(1+x\right)}+\dfrac{1-x}{\left(1-x\right)\left(1+x\right)}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{\left(1+x\right)+\left(1-x\right)}{\left(1-x\right)\left(1+x\right)}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{2}{1-x^2}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{2\left(1+x^2\right)}{\left(1-x^2\right)\left(1+x^2\right)}+\dfrac{2\left(1-x^2\right)}{\left(1-x^2\right)\left(1+x^2\right)}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{2\left(1+x^2\right)+2\left(1-x^2\right)}{\left(1-x^2\right)\left(1+x^2\right)}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{2+2x^2+2-2x^2}{1-x^4}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{4}{1-x^4}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{4\left(1+x^4\right)}{\left(1+x^4\right)\left(1-x^4\right)}+\dfrac{4\left(1-x^4\right)}{\left(1+x^4\right)\left(1-x^4\right)}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{4\left(1+x^4\right)+4\left(1-x^4\right)}{\left(1+x^4\right)\left(1-x^4\right)}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{4+4x^4+4-4x^4}{1-x^8}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{8}{1-x^8}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{8\left(1+x^8\right)}{\left(1-x^8\right)\left(1+x^8\right)}+\dfrac{8\left(1-x^8\right)}{\left(1-x^8\right)\left(1+x^8\right)}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{8\left(1+x^8\right)+8\left(1-x^8\right)}{\left(1-x^8\right)\left(1+x^8\right)}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{8+8x^8+8-8x^8}{1-x^{16}}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{16}{1-x^{16}}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{16\left(1+x^{16}\right)}{\left(1-x^{16}\right)\left(1+x^{16}\right)}+\dfrac{16\left(1-x^{16}\right)}{\left(1-x^{16}\right)\left(1+x^{16}\right)}\)
\(=\dfrac{16\left(1+x^{16}\right)+16\left(1-x^{16}\right)}{\left(1-x^{16}\right)\left(1+x^{16}\right)}\)
\(=\dfrac{16+16x^{16}+16-16x^{16}}{1-x^{32}}\)
\(=\dfrac{32}{1-x^{32}}\)
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rút gọn các phân thức
a,\(\dfrac{7xy^3\left(x-2y\right)}{14x^2y^2\left(x-2y\right)^2}\)
b,\(\dfrac{4a^2-8ab}{2\left(2b-a\right)^3}\)
c,\(\dfrac{3x^3-3x}{x^4-1}\)
d,\(\dfrac{45x\left(3-x\right)}{15x\left(x-3\right)^3}\)
c: \(=\dfrac{3x\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x^2+1\right)}=\dfrac{3x}{x^2+1}\)
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A dfrac{5xy^2-3z}{3xy}+dfrac{4x^2y+3z}{3xy}B dfrac{3y+5}{y-1}+dfrac{-y^2-4y}{1-y}+dfrac{y^2+y+7}{y-1}C dfrac{6x}{x^2-9}+dfrac{5x}{x-3}+dfrac{x}{x+3}D dfrac{1-3x}{2x}+dfrac{3x-2}{2x-1}+dfrac{3x-2}{2x-4x^2}E dfrac{x^3+2x}{x^3+1}+dfrac{2x}{x^2-x+1}+dfrac{1}{x+1}
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A = \(\dfrac{5xy^2-3z}{3xy}+\dfrac{4x^2y+3z}{3xy}\)
B = \(\dfrac{3y+5}{y-1}+\dfrac{-y^2-4y}{1-y}+\dfrac{y^2+y+7}{y-1}\)
C = \(\dfrac{6x}{x^2-9}+\dfrac{5x}{x-3}+\dfrac{x}{x+3}\)
D = \(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)
E = \(\dfrac{x^3+2x}{x^3+1}+\dfrac{2x}{x^2-x+1}+\dfrac{1}{x+1}\)
b: \(B=\dfrac{3y+5}{y-1}-\dfrac{-y^2-4y}{y-1}+\dfrac{y^2+y+7}{y-1}\)
\(=\dfrac{3y+5+y^2+4y+y^2+y+7}{y-1}\)
\(=\dfrac{2y^2+8y+12}{y-1}\)
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1.Tính: \(\left(\dfrac{-2}{3}x^3y^2z\right).5xy^2z^2\)
2. Tính GTBT M= \(\dfrac{2x^2y-1,2\left(3x-2y\right)}{xy}\)tại x=\(\dfrac{1}{2}\); y= 2
2: Thay \(x=\dfrac{1}{2}\) và y=2 vào M, ta được:
\(M=\dfrac{2\cdot\left(\dfrac{1}{2}\right)^2\cdot2-1.2\cdot\left(3\cdot\dfrac{1}{2}-2\cdot2\right)}{\dfrac{1}{2}\cdot2}\)
\(=4\cdot\dfrac{1}{4}-1.2\left(\dfrac{3}{2}-4\right)\)
\(=1-1.8+4.8\)
\(=4\)
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1: Ta có: \(\left(-\dfrac{2}{3}x^3y^2\right)z\cdot5xy^2z^2\)
\(=\left(-\dfrac{2}{3}\cdot5\right)\cdot\left(x^3\cdot x\right)\cdot\left(y^2\cdot y^2\right)\cdot\left(z\cdot z^2\right)\)
\(=\dfrac{-10}{3}x^4y^4z^3\)
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bài 11.rút gọn biểu thức:a,dfrac{9x^2}{11y^2}:dfrac{3x}{2y}:dfrac{6x}{11y} b,dfrac{3x+15y}{x^3-y^3}:dfrac{x+5y}{x-y} c,dfrac{x^2-1}{x^2-4x+4}:dfrac{x+1}{2-x} d,dfrac{5x+10}{x+2}:dfrac{5y}{x} e,dfrac{2x}{3x-3y}:dfrac{x^2}{x-y} f,dfrac{5x-3}{4x^2y}-dfrac{x-3}{4x^2y} g,dfrac{3x+10}{x+3}-dfrac{x+4}{x+3} h,dfrac{4}{x-1}+dfrac{2}{1-x}+dfrac{x}{x-1} i,dfrac{2x^2-x}{x-1}+dfrac{x+1}{1-x}+dfrac{2-x^2}{x-1} j,dfrac{x-2}{x-6}-d...
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bài 11.rút gọn biểu thức:
\(a,\dfrac{9x^2}{11y^2}:\dfrac{3x}{2y}:\dfrac{6x}{11y}\) \(b,\dfrac{3x+15y}{x^3-y^3}:\dfrac{x+5y}{x-y}\)
\(c,\dfrac{x^2-1}{x^2-4x+4}:\dfrac{x+1}{2-x}\) \(d,\dfrac{5x+10}{x+2}:\dfrac{5y}{x}\)
\(e,\dfrac{2x}{3x-3y}:\dfrac{x^2}{x-y}\) \(f,\dfrac{5x-3}{4x^2y}-\dfrac{x-3}{4x^2y}\)
\(g,\dfrac{3x+10}{x+3}-\dfrac{x+4}{x+3}\) \(h,\dfrac{4}{x-1}+\dfrac{2}{1-x}+\dfrac{x}{x-1}\)
\(i,\dfrac{2x^2-x}{x-1}+\dfrac{x+1}{1-x}+\dfrac{2-x^2}{x-1}\) \(j,\dfrac{x-2}{x-6}-\dfrac{x-18}{6-x}+\dfrac{x+2}{x-6}\)
\(k,\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\) \(m,\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
\(n,\dfrac{3}{x+3}-\dfrac{x-6}{x^2+3x}\) \(p,\dfrac{x+3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x^2-3x}\)
f: \(=\dfrac{5x-3-x+3}{4x^2y}=\dfrac{4x}{4x^2y}=\dfrac{1}{xy}\)
g: \(=\dfrac{3x+10-x-4}{x+3}=\dfrac{2x+6}{x+3}=2\)
h: \(=\dfrac{4-2+x}{x-1}=\dfrac{x+2}{x-1}\)
n: \(=\dfrac{3x-x+6}{x\left(x+3\right)}=\dfrac{2\left(x+3\right)}{x\left(x+3\right)}=\dfrac{2}{x}\)
p: \(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}=0\)
k: \(=\dfrac{x-2x-4+x-2}{\left(x+2\right)\left(x-2\right)}=\dfrac{-6}{x^2-4}\)
m: \(=\dfrac{3x-x+6}{x\left(2x+6\right)}=\dfrac{2x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\)
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Quy đồng mẫu hai phân thức:
a) dfrac{5}{2x+6},dfrac{3}{x^2-9} b)dfrac{2x}{x^2-8x+16},dfrac{x}{3x^2-12x}
c)dfrac{x+y}{x}và dfrac{x}{x-y} d)dfrac{2}{x^2+2xy}và dfrac{1}{xy+2y^2}
e)dfrac{1}{x+2},dfrac{8}{2x-x^2} d)x^2+1, dfrac{x^4}{x^2-1}
f)dfrac{x^3}{x^3-3x^2y+3xy^2-y^3},dfrac{x}{y^2-xy}
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Quy đồng mẫu hai phân thức:
a) \(\dfrac{5}{2x+6},\dfrac{3}{x^2-9}\) b)\(\dfrac{2x}{x^2-8x+16},\dfrac{x}{3x^2-12x}\)
c)\(\dfrac{x+y}{x}\)và \(\dfrac{x}{x-y}\) d)\(\dfrac{2}{x^2+2xy}\)và \(\dfrac{1}{xy+2y^2}\)
e)\(\dfrac{1}{x+2},\dfrac{8}{2x-x^2}\) d)\(x^2+1\), \(\dfrac{x^4}{x^2-1}\)
f)\(\dfrac{x^3}{x^3-3x^2y+3xy^2-y^3},\dfrac{x}{y^2-xy}\)
a: \(\dfrac{5}{2x+6}=\dfrac{5\left(x-3\right)}{2\left(x+3\right)\left(x-3\right)}\)
3/x^2-9=6/2(x+3)(x-3)
b: \(\dfrac{2x}{x^2-8x+16}=\dfrac{2x}{\left(x-4\right)^2}=\dfrac{6x^2}{3x\left(x-4\right)^2}\)
\(\dfrac{x}{3x^2-12x}=\dfrac{x}{3x\left(x-4\right)}=\dfrac{x\left(x-4\right)}{3x\left(x-4\right)^2}\)
c: \(\dfrac{x+y}{x}=\dfrac{\left(x+y\right)\cdot\left(x-y\right)}{x\left(x-y\right)}\)
x/x-y=x^2/x(x-y)
e: \(\dfrac{1}{x+2}=\dfrac{2x-x^2}{x\left(x+2\right)\left(2-x\right)}\)
\(\dfrac{8}{2x-x^2}=\dfrac{8\left(x+2\right)}{x\left(2-x\right)\left(2+x\right)}\)
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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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