giải hộ em với ạ câu 1-7 thôi ạ
1: \(\dfrac{b}{6a}-\dfrac{4a+3b^2}{18ab}+\dfrac{x}{9b}\)
\(=\dfrac{b\cdot3b}{6a\cdot3b}-\dfrac{4a+3b^2}{18ab}+\dfrac{x\cdot2a}{9b\cdot2a}\)
\(=\dfrac{3b^2-4a-3b^2+2ax}{18ab}\)
\(=\dfrac{2ax-4a}{18ab}=\dfrac{2a\left(x-2\right)}{18ab}=\dfrac{x-2}{9b}\)
2: \(\dfrac{x}{4a}+\dfrac{6a-5bx}{20ab}-\dfrac{a-1}{10b}\)
\(=\dfrac{x\cdot5b}{4a\cdot5b}+\dfrac{6a-5bx}{20ab}-\dfrac{2a\left(a-1\right)}{2a\cdot10b}\)
\(=\dfrac{5bx+6a-5bx-2a^2+2a}{20ab}\)
\(=\dfrac{-2a^2+8a}{20ab}=\dfrac{-2a\left(a-4\right)}{20ab}=\dfrac{-\left(a-4\right)}{10b}\)
3: \(\dfrac{3}{4x}-\dfrac{10x+7y}{12xy}+\dfrac{5}{6y}\)
\(=\dfrac{3\cdot3y}{4x\cdot3y}-\dfrac{10x+7y}{12xy}+\dfrac{5\cdot2x}{6y\cdot2x}\)
\(=\dfrac{9y-10x-7y+10x}{12xy}=\dfrac{2y}{12xy}=\dfrac{1}{6x}\)
4: \(\dfrac{bc-a^2}{ab}+\dfrac{ac-b^2}{bc}+\dfrac{ab-c^2}{ca}\)
\(=\dfrac{c\left(bc-a^2\right)+a\left(ac-b^2\right)+b\left(ab-c^2\right)}{abc}\)
\(=\dfrac{bc^2-ca^2+a^2c-ab^2+b\left(ab-c^2\right)}{abc}\)
\(=\dfrac{bc^2-ab^2-ca^2+a^2c+b^2a-bc^2}{abc}\)
\(=\dfrac{-ab^2-a^2c+a^2c+ab^2}{abc}=0\)
5: \(\dfrac{1}{2a}-\dfrac{x^2-2ax}{2a\cdot x^2}-\dfrac{2}{x}\)
\(=\dfrac{x^2-\left(x^2-2ax\right)-2\left(2ax\right)}{2a\cdot x^2}\)
\(=\dfrac{2ax-4ax}{2a\cdot x^2}=\dfrac{-2\cdot a\cdot x}{2\cdot a\cdot x\cdot x}=\dfrac{-1}{x}\)
6: \(\dfrac{1}{x}+\dfrac{1}{x+7}+\dfrac{x-1}{x\left(x+7\right)}\)
\(=\dfrac{x+7+x+x-1}{x\left(x+7\right)}\)
\(=\dfrac{3x+6}{x\left(x+7\right)}\)
7: \(\dfrac{-1}{3}+\dfrac{x}{a-2}+\dfrac{a+3x-2}{3a-6}\)
\(=\dfrac{-a+2+3x+a+3x-2}{3a-6}\)
\(=\dfrac{6x}{3a-6}=\dfrac{6x}{3\left(a-2\right)}=\dfrac{2x}{a-2}\)