`|x-1/2| =3/4`

`TH1: x-1/2 = 3/4`

`=>x= 3/4 + 1/2`

`=>x=5/4`

`TH2:x- 1/2 = -3/4`

`=>x= -3/4 + 1/2`

`=>x= -1/4`

Vậy `x in {-1/4 ; 5/4}`

\(a,\dfrac{36\left(x-2\right)^3}{32-16x} =\dfrac{36\left(x-2\right)^3}{16\left(2-x\right)}=\dfrac{4.9\left(x-2\right)\left(x-2\right)^2}{-4.4\left(x-2\right)}=-\dfrac{9\left(x-2\right)^2}{4}\\ =b,\dfrac{x^2-xy}{5y^2-5xy}=\dfrac{x\left(x-y\right)}{5y\left(y-x\right)}=\dfrac{x\left(x-y\right)}{-5y\left(x-y\right)}=-\dfrac{x}{5y}\\ c,\dfrac{x^2-7x+12}{x^2-4x+3}=\dfrac{x^2-3x-4x+12}{x^2-x-3x+3}=\dfrac{x\left(x-3\right)-4\left(x-3\right)}{x\left(x-1\right)-3\left(x-1\right)}=\dfrac{\left(x-3\right)\left(x-4\right)}{\left(x-1\right)\left(x-3\right)}=\dfrac{x-4}{x-1}\)

\(\dfrac{45\left(3-x\right)}{15x\left(x-3\right)^3}\\ =\dfrac{-15.3\left(x-3\right)}{15x\left(x-3\right)\left(x-3\right)^2}\\ =\dfrac{-3}{x\left(x-3\right)^2}\)

`5,1 - 13,8+x=1,8`

`=>5,1+x=1,8+13,8`

`=>5,1+x=15,6`

`=>x=15,6-5,1`

`=>x=10,5`

còn rút gọn được `2` nx nhé

\(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}+\dfrac{1}{195}\\ =\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}+\dfrac{1}{9\times11}+\dfrac{1}{11\times13}+\dfrac{1}{13\times15}\\ =\dfrac{1}{2}\times\left(\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+\dfrac{2}{9\times11}+\dfrac{2}{11\times13}+\dfrac{2}{13\times15}\right)\\ =\dfrac{1}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{13}-\dfrac{1}{15}\right)\\ =\dfrac{1}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{15}\right)\\ =\dfrac{1}{2}\times\dfrac{4}{15}\\ =\dfrac{2}{15}\)

Đặt `4/(x+2y)=a ; 1/(y-2)=b`

Hệ phương trình `<=>{(4a+b=5),(a-b=10):}

`<=>{(a=3),(b=-7):}`

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x+2y}=3\\\dfrac{1}{y-2}=-7\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+2y=\dfrac{1}{3}\\y-2=\dfrac{-1}{7}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+2.\dfrac{13}{7}=\dfrac{1}{3}\\y=\dfrac{13}{7}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-71}{21}\\y=\dfrac{13}{7}\end{matrix}\right.\)

\(\dfrac{6}{x^2+4x}+\dfrac{3}{2x+8}\\ =\dfrac{6}{x\left(x+4\right)}+\dfrac{3}{2\left(x+4\right)}\\ =\dfrac{6.2}{2x\left(x+4\right)}+\dfrac{3.x}{2x\left(x+4\right)}\\ =\dfrac{12+3x}{2x\left(x+4\right)}\\ =\dfrac{3\left(x+4\right)}{2x\left(x+4\right)}\\ =\dfrac{3}{2x}\)

Đổi ` 2 3/5  =13/5`

Diện tích hình vuông là:

`13/5 xx 13/5 = 169/25 (cm^2)`

Đổi `169/25 cm^2 = 6,76cm^2 = 676mm^2`

\(\dfrac{4\times x}{1\times5}+\dfrac{4\times x}{5\times9}+\dfrac{4\times x}{9\times13}+\dfrac{4\times x}{13\times17}=16\\ \Rightarrow x\times\left(\dfrac{4}{1\times5}+\dfrac{4}{5\times9}+\dfrac{4}{9\times13}+\dfrac{4}{13\times17}\right)=16\\ \Rightarrow x\times\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}\right)=16\\ \Rightarrow x\times\left(1-\dfrac{1}{17}\right)=16\\ \Rightarrow x\times\dfrac{16}{17}=16\\ \Rightarrow x=16:\dfrac{16}{17}\\ \Rightarrow x=17\)