Question

1. Rút gọn phân thức: 

a) \(\dfrac{12x^3y^2}{18xy^5}\)          b) \(\dfrac{15x\left(x+5\right)^3}{20x^2\left(x+5\right)}\) 

 

2. Phân tích tử và mẫu thành nhân tử rồi rút gọn phân thức:

 a) \(\dfrac{3x^2-12x+12}{x^4-8x}\)      b) \(\dfrac{7x^2+14x+7}{3x^2+3x}\)

Answer 1

\(1,a,\dfrac{12x^3y^2}{18xy^5}=\dfrac{2x^2}{3y^3}\\ b,\dfrac{15x\left(x+5\right)^3}{20x^2\left(x+5\right)}=\dfrac{3\left(x+5\right)^2}{4x}\\ 2,a,\dfrac{3x^2-12x+12}{x^4-8x}=\dfrac{3\left(x^2-4x+4\right)}{x\left(x^3-8\right)}=\dfrac{3\left(x-2\right)^2}{x\left(x-2\right)\left(x^2+x+2\right)}=\dfrac{3\left(x-2\right)}{x\left(x^2+x+2\right)}\\ b,\dfrac{7x^2+14x+7}{3x^2+3x}=\dfrac{7\left(x^2+2x+1\right)}{3x\left(x+1\right)}=\dfrac{7\left(x+1\right)^2}{3x\left(x+1\right)}=\dfrac{7\left(x+1\right)}{3x}\)

Answer 2

1)

a) \(\dfrac{12x^3y^2}{18xy^5}=\dfrac{2x^2}{3y^3}\)

b) \(\dfrac{15x\left(x+5\right)^3}{20x^2\left(x+5\right)}=\dfrac{3\left(x+5\right)^2}{4x}\)

2)

a) \(\dfrac{3x^2-12x+12}{x^4-8x}\\ =\dfrac{3x^2-6x-6x+12}{x\left(x^3-8\right)}\\ =\dfrac{3x\left(x-2\right)-6\left(x-2\right)}{x\left(x-2\right)\left(x^2+2x+4\right)}\\ =\dfrac{\left(x-2\right)\left(3x-6\right)}{x\left(x-2\right)\left(x^2+2x+4\right)}\\ =\dfrac{3x-6}{x\left(x^2+2x+4\right)}\)

b)

\(\dfrac{7x^2+14x+7}{3x^2+3x}\\ =\dfrac{7x^2+7x+7x+7}{3x\left(x+1\right)}\\ =\dfrac{7x\left(x+1\right)+7\left(x+1\right)}{3x\left(x+1\right)}\\ =\dfrac{\left(x+1\right)\left(7x+7\right)}{3x\left(x+1\right)}\\ =\dfrac{7x+7}{3x}\)

Answer 3

\(1a)\dfrac{12x^3y^2}{18xy^5}=\dfrac{2x^2}{3y^3}\)

\(b)\dfrac{15x\left(x+5\right)^3}{20x^2\left(x+5\right)}=\dfrac{3\left(x+5\right)^2}{4x}\)

\(2a)\dfrac{3x^2-12x+12}{x^4-8x}=\dfrac{3\left(x^2-4x+4\right)}{x\left(x^3-8\right)}=\dfrac{3\left(x-2\right)^2}{x\left(x-2\right)\left(x^2+2x+4\right)}=\dfrac{3\left(x-2\right)}{x\left(x^2+2x+4\right)}\)

\(b)\dfrac{7x^2+14x+7}{3x^2+3x}=\dfrac{7\left(x^2+2x+1\right)}{3x\left(x+1\right)}=\dfrac{7\left(x+1\right)^2}{3x\left(x+1\right)}=\dfrac{7\left(x+1\right)}{3x}\)