Câu 3:
a: \(\dfrac{2x-4}{5}+\dfrac{3x+14}{5}\)
\(=\dfrac{2x-4+3x+14}{5}=\dfrac{5x+10}{5}=x+2\)
b: \(\dfrac{x+1}{x-5}+\dfrac{x-18}{x-5}+\dfrac{x+2}{x-5}\left(x\ne5\right)\)
\(=\dfrac{x+1+x-18+x+2}{x-5}=\dfrac{3x-15}{x-5}=3\)
c: \(\dfrac{4-x^2}{x-3}+\dfrac{2x-2x^2}{3-x}+\dfrac{5-4x}{x-3}\)(ĐKXĐ: x<>3)
\(=\dfrac{4-x^2}{x-3}+\dfrac{2x^2-2x}{x-3}+\dfrac{5-4x}{x-3}\)
\(=\dfrac{4-x^2+2x^2-2x+5-4x}{x-3}\)
\(=\dfrac{x^2-6x+9}{x-3}=x-3\)
d: \(\dfrac{2}{x+2}+\dfrac{-4}{2-x}+\dfrac{5x+2}{4-x^2}\)(ĐKXĐ: \(x\notin\left\{2;-2\right\}\))
\(=\dfrac{2}{x+2}+\dfrac{4}{x-2}-\dfrac{5x+2}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{2x-4+4x+8-5x-2}{\left(x+2\right)\left(x-2\right)}=\dfrac{x+2}{\left(x+2\right)\left(x-2\right)}=\dfrac{1}{x-2}\)
f:
\(\dfrac{x+1}{x-2}\cdot\dfrac{x^2-4}{\left(x+1\right)^2}\)(ĐKXĐ: \(x\notin\left\{2;-1\right\}\))
\(=\dfrac{x+1}{x-2}\cdot\dfrac{\left(x-2\right)\left(x+2\right)}{\left(x+1\right)^2}\)
\(=\dfrac{x+2}{x+1}\)
h: \(\dfrac{3-3x}{x^2-9}\cdot\dfrac{x-3}{x-1}\)(ĐKXĐ: \(x\notin\left\{1;-3;3\right\}\))
\(=\dfrac{-3\left(x-1\right)}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{x-3}{x-1}\)
\(=\dfrac{-3}{x+3}\)
4:
a: Thời gian lúc đi là:
\(\dfrac{120}{x}\left(h\right)\)
Thời gian lúc về là: \(\dfrac{120}{x+5}\left(h\right)\)
b: Tổng thời gian đi và về là: \(\dfrac{120}{x}+\dfrac{120}{x+5}=120\left(\dfrac{1}{x}+\dfrac{1}{x+5}\right)\)
\(=120\cdot\dfrac{x+5+x}{x\left(x+5\right)}=\dfrac{120\left(2x+5\right)}{x\left(x+5\right)}\)(h)
c: Thời gian đi nhiều hơn:
\(\dfrac{120}{x}-\dfrac{120}{x+5}=\dfrac{120x+600-120x}{x\left(x+5\right)}\)
\(=\dfrac{600}{x\left(x+5\right)}\left(h\right)\)
