Question

rút gọn
a) 10xy^2(x+y) / 15xy(x + y)^3
b) x^2 - xy -x + y / x^2 + xy - x- y
c) 3x^2 - 12x + 12 / x^4 - 8x

Answer 1

a,\(\dfrac{10xy^2\left(x+y\right)}{15xy\left(x+y\right)^3}\)

\(=\dfrac{2y}{3\left(x+y\right)^2}\)

b,\(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)

\(=\dfrac{\left(x^2-x\right)+\left(-xy+y\right)}{\left(x^2-x\right)+\left(xy-y\right)}\)

\(=\dfrac{x\left(x-1\right)-y\left(x-1\right)}{x\left(x-1\right)+y\left(x-1\right)}\)

\(=\dfrac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}\)

\(=\dfrac{x-y}{x+y}\)

c,\(\dfrac{3x^2-12x+12}{x^4-8x}\)

\(=\dfrac{3\left(x^2-4x+4\right)}{x\left(x^3-2^3\right)}\)

\(=\dfrac{3\left(x-2\right)^2}{x\left[\left(x-2\right)\left(x^2+2x+4\right)\right]}\)

\(=\dfrac{3\left(x-2\right)}{x\left(x^2+2x+4\right)}\)