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Question

ai giúp mình với mình đang cần gấp ạ undefined

Nguyễn Lê Phước Thịnh · Accepted Answer

a: $\frac{5x-5}{\left(x+1\right)^2}\cdot\frac{3+3x}{20-20x}$

$=\frac{5\left(x-1\right)}{\left(x+1\right)^2}\cdot\frac{3\left(x+1\right)}{-20\left(x-1\right)}$

$=\frac{5}{-20}\cdot\frac{3}{x+1}=\frac{-1}{4}\cdot\frac{3}{x+1}=\frac{-3}{4x+4}$

b: $\frac{x+4}{5x-25}\cdot\frac{x-5}{x^2+8x+16}$

$=\frac{x+4}{5\left(x-5\right)}\cdot\frac{x-5}{\left(x+4\right)^2}$

$=\frac{1}{5\left(x+4\right)}$

c: $\frac{x^2+xy}{5x^2-5y^2}\cdot\frac{3x^3-3y^3}{x^2-xy}$

$=\frac{x\left(x+y\right)}{5\left(x^2-y^2\right)}\cdot\frac{3\left(x^3-y^3\right)}{x\left(x-y\right)}$

$=\frac{x+y}{x-y}\cdot\frac{3\left(x-y\right)\left(x^2+xy+y^2\right)}{5\left(x-y\right)\left(x+y\right)}=\frac{3\left(x^2+xy+y^2\right)}{5\left(x-y\right)}$

d: $\frac{x^2y^2-4y^2}{4xy}\cdot\frac{x^2y}{2xy-x^2y}$

$=\frac{y^2\left(x^2-4\right)}{4xy}\cdot\frac{x^2y}{xy\left(2-x\right)}=\frac{-x^2y^3}{4xy\cdot xy}\cdot\frac{\left(x-2\right)\left(x+2\right)}{x-2}$

$=-\frac{y}{4}\cdot\left(x+2\right)=\frac{-y\left(x+2\right)}{4}$

e: $\frac{2x^3-2y^3}{3x+3y}\cdot\frac{15x^2-15y^2}{x^2+xy+y^2}$

$=\frac{2\left(x^3-y^3\right)}{3\left(x+y\right)}\cdot\frac{15\left(x^2-y^2\right)}{x^2+xy+y^2}$

$=\frac{30}{3}\cdot\frac{\left(x-y\right)\left(x^2+xy+y^2\right)\cdot\left(x-y\right)\left(x+y\right)}{\left(x+y\right)\left(x^2+xy+y^2\right)}=10\left(x-y\right)^2$

f: $\frac{x^4-y^4}{x^2-2xy+y^2}\cdot\frac{x-y}{xy+x^2}$

$=\frac{\left(x^2-y^2\right)\left(x^2+y^2\right)}{\left(x-y\right)^2}\cdot\frac{x-y}{x\left(x+y\right)}=\frac{\left(x-y\right)\left(x+y\right)}{\left(x-y\right)^2}\cdot\frac{\left(x^2+y^2\right)\left(x-y\right)}{x\left(x+y\right)}$

$=\frac{x^2+y^2}{x}$

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