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Bài giải:
a) 5x2y4 : 10x2y = 510510x2 – 2. y4 – 1 = 1212y3
b) 3434x3y3 : (- 1212x2y2) = 3434 . (-2) . x3 – 2 . y3 – 2 = -3232xy
c) (-xy)10 : (-xy)5 = (-xy)10 – 5 = (-xy)5 = -x5y5.
Bài giải:
15x4y3z2 : 5xy2z2 với x = 2, y = -10, z = 2004
Ta có 15x4y3z2 : 5xy2z2 = 3 . x4 – 1 . y3 – 2 . z2 – 2 = 3x3y
Tại x = 2, y = -10, z = 2004
Ta được: 3 . 23(-10) = 3 . 8 . (-10) = -240.

(x-6)(x+6)/2x+10 * -3(x-6)= 3x+18/2x+10
(x-3y)(x+3y)/x^2y^2* 3xy/2(x-3y)=3x+9y/2xy
3(x-y)(x+y)/5xy * -15x^2y/2(X-y)=-9x/2


a: \(\frac{x+1}{x-y}+\frac{x-1}{x-y}+\frac{x+3}{x-y}\)
\(=\frac{x+1+x-1+x+3}{x-y}=\frac{3x+3}{x-y}\)
b: \(\frac{5xy^2-3z}{3xy}+\frac{4x^2y+3z}{3xy}=\frac{5xy^2-3z+4x^2y+3z}{3xy}\)
\(=\frac{5xy^2+4x^2y}{3xy}=\frac{xy\left(5y+4x\right)}{3xy}=\frac{4x+5y}{3}\)
c: \(\frac{x+9}{x^2-9}-\frac{3}{x^2+3x}\)
\(=\frac{x+9}{\left(x-3\right)\left(x+3\right)}-\frac{3}{x\left(x+3\right)}\)
\(=\frac{x\left(x+9\right)-3\left(x-3\right)}{x\left(x+3\right)\left(x-3\right)}=\frac{x^2+9x-3x+9}{x\left(x+3\right)\left(x-3\right)}\)
\(=\frac{x^2+6x+9}{x\left(x+3\right)\left(x-3\right)}=\frac{\left(x+3\right)^2}{x\left(x+3\right)\left(x-3\right)}=\frac{x+3}{x\left(x-3\right)}\)
d: \(\frac{x}{5x+5}-\frac{x-10}{10x-10}\)
\(=\frac{x}{5\left(x+1\right)}-\frac{x-10}{10\left(x-1\right)}\)
\(=\frac{2x\left(x-1\right)-\left(x-10\right)\left(x+1\right)}{10\left(x-1\right)\left(x+1\right)}=\frac{2x^2-2x-\left(x^2+x-10x-10\right)}{10\left(x-1\right)\left(x+1\right)}\)
\(=\frac{2x^2-2x-x^2+9x+10}{10\left(x-1\right)\left(x+1\right)}=\frac{x^2+7x+10}{10\left(x-1\right)\left(x+1\right)}\)


\(\frac{y}{xy-5x^2}-\frac{15x-25x}{y^2-25x^2}\)
ĐKXĐ : \(\hept{\begin{cases}x,y\ne0\\y\ne\pm5x\end{cases}}\)
\(=\frac{y}{x\left(y-5x\right)}-\frac{-10x}{\left(y-5x\right)\left(y+5x\right)}\)
\(=\frac{y\left(y+5x\right)}{x\left(y-5x\right)\left(y+5x\right)}-\frac{-10xx}{x\left(y-5x\right)\left(y+5x\right)}\)
\(=\frac{y^2+5xy+10x^2}{x\left(y-5x\right)\left(y+5x\right)}\)
\(\frac{y}{xy-5x^2}-\frac{-10x}{y^2-25x^2}=\frac{y^3-25x^2y}{\left(xy-5x^2\right)\left(y^2-25x^2\right)}-\frac{-10x^2y+50x^3}{\left(y^2-25x^2\right)\left(xy-5x^2\right)}\)
\(=\frac{y^3-25x^2y+10x^2y-50x^3}{\left(xy-5x^2\right)\left(y^2-25x^2\right)}=\frac{y^3-15x^2y-50x^3}{\left(xy-5x^2\right)\left(y^2-25x^2\right)}=\frac{y^3-50x^3}{x\left(y-5x\right)^2\left(y+5x\right)}\)
15x2y2 : 5xy2 = (15:5).(x2 : x).(y2 : y2 ) = 3.x(2-1).1 = 3x