rút gọn phân thức sau \(\frac{18x^3y^5}{27xy^8}\)
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\(\frac{14xy^5\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}=\frac{2y^4}{3x\left(2x-3y\right)}\)

1/ x3 + x2y - x2z -xyz
= x2(x + y) - xz(x + y)
= (x + y) (x2 - xz)
= x (x + y) (x - z)
2/ 3x3y - 18x2y2 + 27xy3
= 3xy(x2 - 6xy + y2)

\(=\frac{2.7.xy.y^5\left(2x-3y\right)}{3.7.xy.x\left(2x-3y\right)^2}=\frac{2y^5}{3x\left(2x-3y\right)}\)
\(\frac{14xy^5\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}\)
\(=\frac{2y^4}{3x\left(2x-3y\right)}\)

A=(8xy-6x^2)/(12y^2-9xy)
A=2x(4y-3x)/3y(4y-3x)
A=2x/3y
B=(2x^3-18x)/(x^4-81)
B=2x(x^2-9)/(x^2-9)(x^2+9)
B=2x/(x^2+9)
C=(x^2-x-30)/(x^2-25)
C=(x^2+6x-5x-30)/(x^2-25)
C=(x(x+6)-5(x+6))/(x-5)(x+5)
C=(x+6)(x-5)/(x-5)(x+5)
C=(x+6)/(x+5)

a) \(3\sqrt{2x}-4\sqrt{2x}+8-2\sqrt{x}\)
\(=-\left(4\sqrt{2x}-3\sqrt{2x}\right)+8-2\sqrt{x}\)
\(=-\sqrt{2x}-2\sqrt{x}+8\)
b) \(3\sqrt{2x}-\sqrt{72x}+3\sqrt{18x}+18\)
\(=3\sqrt{2x}-6\sqrt{2x}+3\cdot3\sqrt{2x}+18\)
\(=3\sqrt{2x}-6\sqrt{2x}+9\sqrt{2x}+18\)
\(=\left(3+9-6\right)\sqrt{2x}+18\)
\(=6\sqrt{2x}+18\)

\(\frac{2x^4+6x^3+18x^2}{x^4-27x}=\frac{2x^2.\left(x^2+3x+9\right)}{x.\left(x^3-27\right)}\)
\(=\frac{2x^2.\left(x^2+3x+9\right)}{x.\left(x-3\right)\left(x^2+3x+9\right)}=\frac{2x}{x-3}\)
2x2/3x3