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\(\dfrac{x^2y}{2};\dfrac{x}{-5^2};\dfrac{-4}{5}\)
a: \(=\left(\dfrac{x}{y\left(x-y\right)}-\dfrac{2x-y}{x\left(x-y\right)}\right):\dfrac{x+y}{xy}\)
\(=\dfrac{x^2-2xy+y^2}{xy\left(x-y\right)}\cdot\dfrac{xy}{x+y}\)
\(=\dfrac{\left(x-y\right)^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{x-y}{x+y}\)
b: \(=\dfrac{x^2+2xy+y^2-x^2+2xy-y^2+4y^2}{2\left(x-y\right)\left(x+y\right)}\cdot\dfrac{x-y}{2y}\)
\(=\dfrac{4xy+4y^2}{2\left(x+y\right)}\cdot\dfrac{1}{2y}=\dfrac{4y\left(x+y\right)}{4y\left(x+y\right)}=1\)
\(a,\frac{x}{xy-y^2}+\frac{2x-y}{xy-x^2}:\left(\frac{1}{x}+\frac{1}{y}\right)\)
\(=\left(\frac{x}{y\left(x-y\right)}+\frac{y-2x}{x\left(x-y\right)}\right):\left(\frac{y}{xy}+\frac{x}{xy}\right)\)
\(=\left(\frac{x-y}{x\left(x-y\right)}\right):\left(\frac{x+y}{xy}\right)\)
\(=\frac{1}{x}.\frac{xy}{x+y}=\frac{y}{x+y}\)
\(B=\left(\dfrac{1}{x^2-xy}-\dfrac{3y^2}{x^4-xy^3}-\dfrac{y}{x^2+x^2y+xy^2}\right).\left(y+\dfrac{x^2}{x+y}\right)\)
\(B=\left(\dfrac{1}{x\left(x-y\right)}-\dfrac{3y^2}{x\left(x^3-y^3\right)}-\dfrac{y}{x\left(x^2+xy+y\right)}\right).\left(y+\dfrac{x^2}{x+y}\right)\)
\(B=\left(\dfrac{1}{x\left(x-y\right)}-\dfrac{3y^2}{x\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{y}{x\left(x^2+xy+y^2\right)}\right).\left(y+\dfrac{x^2}{x+y}\right)\)
\(B=\left(\dfrac{x^2+xy+y^2}{x\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{3y^2}{x\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{y\left(x-y\right)}{x\left(x^2+xy+y^2\right)}\right).\left(y+\dfrac{x^2}{x+y}\right)\)
\(B=\left(\dfrac{x^2+xy+y^2-3y^2-xy+y^2}{x\left(x-y\right)\left(x^2+xy+y^2\right)}\right).\left(y+\dfrac{x^2}{x+y}\right)\)
\(B=\dfrac{x^2+2y^2-3y^2}{x\left(x-y\right)\left(x^2+xy+y^2\right)}.\left(y+\dfrac{x^2}{x+y}\right)\)
\(B=\dfrac{x^2+2y^2-3y^2}{x\left(x-y\right)\left(x^2+xy+y^2\right)}.\left(\dfrac{y\left(x+y\right)}{x+y}+\dfrac{x^2}{x+y}\right)\)
\(B=\dfrac{x^2+2y^2-3y^2}{x\left(x-y\right)\left(x^2+xy+y^2\right)}.\dfrac{x^2+xy+y^2}{x+y}\)
\(B=\dfrac{x^2+2y^2-3y^2}{x\left(x^2-y^2\right)}\)
1)\(25x^2y^4+30xy^2z+9z^2=\left(5xy^2+3z\right)^2\)
\(\dfrac{16}{9}x^2+4xyz^2+\dfrac{9}{4}y^2z^4=\left(\dfrac{4}{3}x+\dfrac{3}{2}yz^2\right)^2\)
2)
a)\(\dfrac{9}{25}x^2+\dfrac{12}{35}xy+\dfrac{4}{49}y^2=\left(\dfrac{3}{5}x+\dfrac{2}{7}y\right)^2=\left(\dfrac{3}{5}.5+\dfrac{2}{7}.\left(-7\right)\right)^2=\left(3-2\right)^2=1\)b)\(\dfrac{25}{16}u^4v^2+\dfrac{1}{5}u^2v^3+\dfrac{4}{625}v^4\)
\(=\left(\dfrac{5}{4}u^2v+\dfrac{2}{25}v^2\right)^2=\left(\dfrac{5}{4}.\dfrac{4}{25}.\left(-5\right)+\dfrac{2}{25}.\left(-5\right)^2\right)^2\)
\(=\left(-1+2\right)^2=1\)
x^2y/2;x/-5^2;-4/5
Thanks youu