\(25\%+0,75\cdot2+\dfrac{1}{9}-\dfrac{3}{4}\\ =0,25+1,5-0,75+\dfrac{1}{9}\\ =1,75-0,75+\dfrac{1}{9}\\ =1+\dfrac{1}{9}\\ =\dfrac{10}{9}\)

\(\dfrac{1}{2}:\dfrac{9}{7}-\dfrac{1}{2}:\dfrac{2}{7}\\ =\dfrac{1}{2}\cdot\dfrac{7}{9}-\dfrac{1}{2}\cdot\dfrac{7}{2}\\ =\dfrac{7}{18}-\dfrac{7}{4}\\ =-\dfrac{49}{36}\)

\(\dfrac{1}{9}:\dfrac{9}{7}-\dfrac{1}{2}:\dfrac{2}{7}\\ =\dfrac{1}{9}\cdot\dfrac{7}{9}-\dfrac{1}{2}\cdot\dfrac{7}{2}\\ =\dfrac{7}{81}-\dfrac{7}{4}\\ =-\dfrac{539}{324}\)

Gọi chiều rộng, chiều rộng hình chữ nhật là: \(x,x+1\) (Điều kiện: \(x\in N\))

Theo đề bài, ta có: Chiều dài, chiều rộng là hai số tự nhiên liên tiếp

\(2\times\left(x+x+1\right)=1998\\ 2\times x+1=1998:2\\ 2\times x+1=999\\ 2\times x=998\\ x=998:2\\ x=499\)

\(\rightarrow\) Chiều dài hình chữ nhật là: \(499+1=500\left(m\right)\)

Đáp số: Chiều dài : \(500m\) chiều rộng \(499m\)

Ta có:

\(5⋮5\)

\(5^2⋮5\)

\(...\)

\(5^{20}⋮5\)

\(\rightarrow C=5+5^2+5^3+...+5^{20}⋮5\left(đpcm\right)\)

\(5x=x+29-36:4\\ \Rightarrow5x=x+29-9\\ \Rightarrow5x=x+20\\ \Rightarrow5x-x=20\\ \Rightarrow4x=20\\ \Rightarrow x=5\)

\(\dfrac{4}{3}\cdot\dfrac{9}{8}:\dfrac{5}{3}\cdot\dfrac{4}{25}\\ =\left(\dfrac{4}{3}\cdot\dfrac{9}{8}\right)\cdot\left(\dfrac{3}{5}\cdot\dfrac{4}{25}\right)\\ =\dfrac{3}{2}\cdot\dfrac{12}{125}\\ =\dfrac{18}{125}\)

\(h,\dfrac{2}{5}x\left(y-1\right)-\dfrac{2}{5}y\left(y-1\right)=\left(\dfrac{2}{5}x-\dfrac{2}{5}y\right)\left(y-1\right)=\dfrac{2}{5}\left(x-y\right)\left(y-1\right)\)

\(l,3x\left(y+2\right)-3\left(y+2\right)=\left(3x-3\right)\left(y+2\right)=3\left(x-1\right)\left(y+2\right)\)

\(đ,5x^2\left(x-2y\right)-15x\left(x-2y\right)=\left(5x^2-15\right)\left(x-2y\right)=5\left(x^2-3\right)\left(x-2y\right)\)

\(e,3\left(x-y\right)-5x\left(x-y\right)=\left(3-5x\right)\left(x-y\right)\)

\(f,x^2-3x=x\cdot x-3\cdot x=x\cdot\left(x-3\right)\)

\(g,6x^2y+4xy^2+2xy=2xy\cdot3x+2xy\cdot2y+2xy\cdot1=2xy\cdot\left(3x+2y+1\right)\)

\(a,4x^2-6x =2x\cdot2x-2x\cdot3=2x\cdot\left(2x-3\right)\)

\(b,9x^3y^2+3x^2y^2=3x^2y^2\cdot3x+3x^2y^2=3x^2y^2\left(3x+1\right)\)

\(c,x^3+2x^2-3x=x\cdot x^2+x\cdot2x-x\cdot3=x\cdot\left(x^2+2x-3\right)\)

\(d,3x-6y=3\cdot x-3\cdot2y=3\cdot\left(x-2y\right)\)