\(6x-5=613\)

\(\Leftrightarrow6x=613+5\)

\(\Leftrightarrow6x=618\)

\(\Leftrightarrow x=103\)

trùng

thiếu

a) \(\dfrac{x^2-16}{4x-x^2}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left(4-x\right)}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left[-\left(x-4\right)\right]}\)

\(=\dfrac{\left(-1\right)\left(x+4\right)}{x}=\dfrac{-x-4}{x}\)

b) \(\dfrac{x^2+4x+3}{2x+6}=\dfrac{x^2+3x+x+3}{2\left(x+3\right)}=\dfrac{x\left(x+3\right)+\left(x+3\right)}{2\left(x+3\right)}\)

\(=\dfrac{\left(x+1\right)\left(x+3\right)}{2\left(x+3\right)}=\dfrac{x+1}{2}\)

c) \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\dfrac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}\)

\(=\dfrac{8\left(x-y\right)}{10\left(x-y\right)}=\dfrac{8}{10}=\dfrac{4}{5}\)

d) \(\dfrac{2ax^2-4ax+2a}{5b-5bx^2}=\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-x^2\right)}=\dfrac{2a\left(x-1\right)^2}{5b\left[-\left(x-1\right)\right]\left(1+x\right)}\)

\(=\dfrac{2a\left[-\left(x-1\right)\right]}{5b\left(1+x\right)}=-\dfrac{2ax-2a}{50\left(1+x\right)}=-\dfrac{-\left(2a-2ax\right)}{5b\left(1+x\right)}-\dfrac{2a-2ax}{5b-5bx}\)

e) \(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}=\dfrac{\left(x+y-z\right)\left(x+y+z\right)}{x+y+z}=z+y-z\)

f) \(\dfrac{4x^2-4xy}{5x^3-5x^2y}=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4x}{5x^2}=\dfrac{4}{5x}\)

áp dụng cái gì để tính...

\(\left(x+\dfrac{1}{3}\right)^3=-\dfrac{1}{8}\)

\(\Leftrightarrow\left(x+\dfrac{1}{3}\right)^3=\left(-\dfrac{1}{2}\right)^3\)

\(\Leftrightarrow x+\dfrac{1}{3}=-\dfrac{1}{2}\)

\(\Leftrightarrow x=-\dfrac{1}{2}-\dfrac{1}{3}\)

\(\Leftrightarrow x=-\dfrac{5}{6}\)

Vậy \(x=-\dfrac{5}{6}\)

\(\dfrac{9}{10}-\dfrac{1}{90}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\)

\(=\dfrac{9}{10}-\left(\dfrac{1}{90}+\dfrac{1}{72}+\dfrac{1}{56}+\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\right)\)

\(=\dfrac{9}{10}-\left(\dfrac{1}{9\cdot10}+\dfrac{1}{9\cdot8}+\dfrac{1}{7\cdot8}+\dfrac{1}{7\cdot6}+\dfrac{1}{5\cdot6}-\dfrac{1}{5\cdot4}-\dfrac{1}{3\cdot4}-\dfrac{1}{3\cdot2}-\dfrac{1}{1\cdot2}\right)\)

\(=\dfrac{9}{10}-\left(\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{8}-\dfrac{1}{9}+...+1-\dfrac{1}{2}\right)\)

\(=\dfrac{9}{10}-\left(1-\dfrac{1}{10}\right)\)

\(=\dfrac{9}{10}-\dfrac{9}{10}\)

\(=0\)

a) \(4x^2-5x+1=4x^2-x-4x+1\)

\(=x\left(4x-1\right)-\left(4x-1\right)=\left(4x-1\right)\left(x-1\right)\)

b) \(7x-3x^2-2=-3x^2+7x-2\)

\(=-3x^2+x+6x-2=-x\left(3x-1\right)+2\left(3x-1\right)\)

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

c) \(x^2-6x+8=x^2-2x-4x+8\)

\(=x\left(x-2\right)-4\left(x-2\right)=\left(x-2\right)\left(x-4\right)\)

d) \(4x^2-4x+3=4x^2-2x-6x+3\)

\(=2x\left(2x-1\right)-3\left(2x-1\right)=\left(2x-1\right)\left(2x-3\right)\)

e) \(3x^2-8x+4=3x^2-6x-2x+4\)

\(=3x\left(x-2\right)-2\left(x-2\right)=\left(x-2\right)\left(3x-2\right)\)

f) \(x^2-21x+38=x^2-2x-19x+38\)

\(=x\left(x-2\right)-19\left(x-2\right)=\left(x-19\right)\left(x-2\right)\)

\(x^5-5x^3+4x\)

\(=x^5-x^3-4x^3+4x\)

\(=x\left(x^4-x^2-4x^2+4\right)\)

\(=x\left(x^2-4\right)\left(x^2-1\right)\)

\(=x\left(x+2\right)\left(x-2\right)\left(x+1\right)\left(x-1\right)\)

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