Question

rút gọn phân thức

a.\(\dfrac{5x-15}{4x+4}:\dfrac{x^2-9}{x^2+2x+1}\)

b.\(\dfrac{6x+48}{7x-7}:\dfrac{x^2-64}{x^2-2x+1}\)

c.\(\dfrac{4x-24}{5x+5}:\dfrac{x^2-36}{x^2+2x+1}\)

d.\(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)

Answer 1

a.\(\dfrac{5\left(x-3\right)}{4\left(x+1\right)}\) : \(\dfrac{\left(x-3\right)\left(x+3\right)}{\left(x+1\right)^2}\)

= \(\dfrac{5\left(x-3\right)}{4\left(x+1\right)}\). \(\dfrac{\left(x+1\right)^2}{\left(x-3\right)\left(x+3\right)}\)

= \(\dfrac{5\left(x+1\right)}{4\left(x+3\right)}\)

b. \(\dfrac{6\left(x+8\right)}{7\left(x-1\right)}\). \(\dfrac{\left(x-1\right)^2}{\left(x-8\right)\left(x+8\right)}\)

= \(\dfrac{6\left(x-1\right)}{7\left(x-8\right)}\)

c.Tương tự hai câu trên nka!!

d. (\(\dfrac{1}{x\left(x+1\right)}\)-\(\dfrac{2-x}{x+1}\)).(\(\dfrac{x}{x-1}\))

=( \(\dfrac{1}{x\left(x+1\right)}\)-\(\dfrac{2x-x^2}{x\left(x+1\right)}\)). ....

= \(\dfrac{\left(1-x\right)^2}{x\left(x+1\right)}\). ...

= \(\dfrac{x-1}{x+1}\)

Answer 2

Lê Cẩm TúThiên ThảoPhạm Thái DươnMai LinhgGuyoSky SơnTùngKhôi Bùi Mysterious PersonPhong ThầnPhùng Khánh Linhtran nguyen baNguyễn Xuân Sángo quanDƯƠNG PHAN KHDũng NguyễnÁNH DƯƠNGlê thị hương giang

Answer 3

c: \(=\dfrac{4\left(x-6\right)}{5\left(x+1\right)}\cdot\dfrac{\left(x+1\right)^2}{\left(x-6\right)\left(x+6\right)}=\dfrac{4\left(x+1\right)}{5\left(x+6\right)}\)

a: \(=\dfrac{5\left(x-3\right)}{4\left(x+1\right)}\cdot\dfrac{\left(x+1\right)^2}{\left(x-3\right)\left(x+3\right)}=\dfrac{5\left(x+1\right)}{4\left(x+3\right)}\)

b: \(=\dfrac{6\left(x+8\right)}{7\left(x-1\right)}\cdot\dfrac{\left(x-1\right)^2}{\left(x-8\right)\left(x+8\right)}=\dfrac{6\left(x-1\right)}{7\left(x-8\right)}\)