Question

[Ánh Vũ Ngọc]

1, Rút gọn các phân thức sau :

a, \(\dfrac{5x}{10}\)

b, \(\dfrac{4xy}{2y}\) ( y # 0)

c, \(\dfrac{21x^2y^3}{6xy}\) ( xy # 0)

d, \(\dfrac{2x+2y}{4}\)

e, \(\dfrac{5x-5y}{3x-3y}\) ( x # y)

f, \(\dfrac{-15x\left(x-y\right)}{3\left(y-x\right)}\) ( x # y)

2, Rút gọn các phân thức sau :

a, \(\dfrac{x^2-16}{4x-x^2}\) ( x # 0, x # 4)

b, \(\dfrac{x^2+4x+3}{2x+6}\) ( x # -3)

c, \(\dfrac{15x\left(x+3\right)^3}{5y\left(x+y\right)^2}\) ( y + ( x+y) # 0)

d, \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}\) ( x # y)

e, \(\dfrac{2x+2y+5x+5y}{2x+2y-5x-5y}\) (x # -y)

Answer 1

[Hà Linh]

1)

a) \(\dfrac{5x}{10}=\dfrac{x}{2}\)

b) \(\dfrac{4xy}{2y}=2x\left(y\ne0\right)\)

c) \(\dfrac{21x^2y^3}{6xy}=\dfrac{7xy^2}{2}\left(xy\ne0\right)\)

d) \(\dfrac{2x+2y}{4}=\dfrac{2\left(x+y\right)}{4}=\dfrac{x+y}{2}\)

e) \(\dfrac{5x-5y}{3x-3y}=\dfrac{5\left(x-y\right)}{3\left(x-y\right)}=\dfrac{5}{3}\left(x\ne y\right)\)

f) \(\dfrac{-15x\left(x-y\right)}{3\left(y-x\right)}=-5x\dfrac{x-y}{y-x}=-5x\dfrac{x-y}{-\left(x-y\right)}\)

\(=-5x.\left(-1\right)=5x\left(x\ne y\right)\)

2)

a) Nhớ ghi ĐK vào nhá, lười quá :V\(\dfrac{x^2-16}{4x-x^2}=-\dfrac{\left(x-4\right)\left(x+4\right)}{x^2-4x}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left(x-4\right)}=\dfrac{x+4}{x}\)

b) \(\dfrac{x^2+4x+3}{2x+6}=\dfrac{x^2+3x+x+3}{2\left(x+3\right)}=\dfrac{x\left(x+3\right)+\left(x+3\right)}{2\left(x+3\right)}\)

\(=\dfrac{\left(x+3\right)\left(x+1\right)}{2\left(x+3\right)}=\dfrac{x+1}{2}\)

c) \(\dfrac{15x\left(x+3\right)^3}{5y\left(x+y\right)^2}=\dfrac{3x\left(x+3\right)^3}{y\left(x+y\right)^2}\) ( câu này có gì đó sai sai )

d) \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\dfrac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}\)

\(=\dfrac{8\left(x-y\right)}{10\left(x-y\right)}=\dfrac{8}{10}=\dfrac{4}{5}\)

e) \(\dfrac{2x+2y+5x+5y}{2x+2y-5x-5y}=\dfrac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}\)

\(=\dfrac{7\left(x+y\right)}{-3\left(x+y\right)}=-\dfrac{7}{3}\)