Bài 8:
a: \(\dfrac{x-4}{x^3-3x^2+x-3}:A=\dfrac{x^2-5x+4}{\left(x-2\right)\left(x-3\right)}\)
=>\(\dfrac{x-4}{\left(x-3\right)\left(x^2+1\right)}:A=\dfrac{\left(x-1\right)\left(x-4\right)}{\left(x-2\right)\left(x-3\right)}\)
=>\(A=\dfrac{x-4}{\left(x-3\right)\left(x^2+1\right)}:\dfrac{\left(x-1\right)\left(x-4\right)}{\left(x-2\right)\left(x-3\right)}\)
=>\(A=\dfrac{x-4}{\left(x-3\right)\left(x^2+1\right)}\cdot\dfrac{\left(x-2\right)\left(x-3\right)}{\left(x-1\right)\left(x-4\right)}\)
=>\(A=\dfrac{x-2}{\left(x^2+1\right)\left(x-1\right)}\)
b: \(\dfrac{\left(x-1\right)^2-6\left(x-1\right)+9}{3x^2-3x}\cdot D=\dfrac{x^2-16}{3x^3-3x}\)
=>\(\dfrac{\left(x-1-3\right)^2}{3x\left(x-1\right)}\cdot D=\dfrac{\left(x-4\right)\left(x+4\right)}{3x\left(x^2-1\right)}\)
=>\(D\cdot\dfrac{\left(x-4\right)^2}{3x\left(x-1\right)}=\dfrac{\left(x-4\right)\left(x+4\right)}{3x\left(x-1\right)\left(x+1\right)}\)
=>\(D=\dfrac{\left(x-4\right)\left(x+4\right)}{3x\left(x-1\right)\left(x+1\right)}:\dfrac{\left(x-4\right)^2}{3x\left(x-1\right)}\)
=>\(D=\dfrac{\left(x-4\right)\left(x+4\right)}{3x\left(x-1\right)\left(x+1\right)}\cdot\dfrac{3x\left(x-1\right)}{\left(x-4\right)^2}=\dfrac{x+4}{\left(x-4\right)\left(x+1\right)}\)
Bài 7:
a: Vận tốc dự định là \(\dfrac{80}{x}\left(\dfrac{km}{h}\right)\)
b: Thời gian thực tế là x-1(giờ)
Vận tốc thực tế là \(\dfrac{80}{x-1}\left(\dfrac{km}{h}\right)\)
c: vận tốc tăng thêm là: \(\dfrac{80}{x-1}-\dfrac{80}{x}=\dfrac{80x-80x+80}{x\left(x-1\right)}=\dfrac{80}{x\left(x-1\right)}\left(\dfrac{km}{h}\right)\)
