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

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

3) \(4x^2-9=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\)

4) \(9-25x^2=3^2-\left(5x\right)^2=\left(3-5x\right)\left(3+5x\right)\)

5) \(4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\)

6) \(9x^2-36=\left(3x\right)^2-6^2=\left(3x-6\right)\left(3x+6\right)\)

7) \(\left(3x\right)^2-y^2=\left(3x+y\right)\left(3x-y\right)\)

8) \(x^2-\left(2y\right)^2=\left(x+2y\right)\left(x-2y\right)\)

9) \(\left(2x\right)^2-y^2=\left(2x-y\right)\left(2x+y\right)\)

\(3x-\dfrac{3}{5}=\dfrac{-7}{10}\\ 3x=\dfrac{-7}{10}+\dfrac{3}{5}\\ 3x=\dfrac{-7}{10}+\dfrac{6}{10}\\ 3x=\dfrac{-1}{10}\\ x=\dfrac{-1}{30}\)

___________________

\(\dfrac{2}{3}+\dfrac{1}{3}:x=\dfrac{3}{5}\\ \dfrac{1}{3}:x=\dfrac{3}{5}-\dfrac{2}{3}\\ \dfrac{1}{3}:x=\dfrac{9}{15}-\dfrac{10}{15}\\ \dfrac{1}{3}:x=\dfrac{-1}{15}\\ x=\dfrac{1}{3}:\dfrac{-1}{15}\\ x=-5\)

\(3x-\dfrac{3}{5}=-\dfrac{7}{10}\)

\(3x\)        \(=-\dfrac{7}{10}+\dfrac{3}{5}\)

\(3x\)        \(=-\dfrac{1}{10}\)

 \(x\)         \(=-\dfrac{1}{10}:3\)

 \(x\)         \(=-\dfrac{1}{30}\)

Vậy \(x=-\dfrac{1}{30}\)

\(\dfrac{2}{3}+\dfrac{1}{3}:x=\dfrac{3}{5}\)

        \(\dfrac{1}{3}:x=\dfrac{3}{5}-\dfrac{2}{3}\)

        \(\dfrac{1}{3}:x=-\dfrac{1}{15}\)

              \(x=\dfrac{1}{3}:-\dfrac{1}{15}\)

              \(x=-5\)

Vậy \(x=-5\)

\(\left(\dfrac{2}{7}-\dfrac{9}{4}\right)-\left(-\dfrac{3}{7}+\dfrac{5}{4}\right)-\left(\dfrac{2}{4}-\dfrac{9}{7}\right)\)

\(=\dfrac{2}{7}-\dfrac{9}{4}+\dfrac{3}{7}-\dfrac{5}{4}-\dfrac{2}{4}+\dfrac{9}{7}\)

\(=\left(\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{9}{7}\right)-\left(\dfrac{9}{4}+\dfrac{5}{4}+\dfrac{2}{4}\right)\)

\(=2-4\)

\(=-2\)

-2

\(\dfrac{4}{7}+\dfrac{3}{7}x=\dfrac{1}{2}\\ \dfrac{3}{7}x=\dfrac{1}{2}-\dfrac{4}{7}\\ \dfrac{3}{7}x=-\dfrac{1}{14}\\ x=-\dfrac{1}{14}:\dfrac{3}{7}\\ x=-\dfrac{1}{6}\)

Vậy....

\(\dfrac{17}{6}-\left(x+\dfrac{7}{6}\right)=\dfrac{7}{4}\\x+\dfrac{7}{6}=\dfrac{17}{6}-\dfrac{7}{4}\\ x+\dfrac{7}{6}=\dfrac{13}{12}\\ x=\dfrac{13}{12}-\dfrac{7}{6}\\ x=-\dfrac{1}{12} \)

Vậy....

\(\dfrac{4}{7}+\dfrac{3}{7}x=\dfrac{1}{2}\\ \Rightarrow\dfrac{3}{7}x=\dfrac{1}{2}-\dfrac{4}{7}\\ \Rightarrow\dfrac{3}{7}x=-\dfrac{1}{14}\\ \Rightarrow x=-\dfrac{1}{14}:\dfrac{3}{7}\\ \Rightarrow x=-\dfrac{1}{6}\)

___________

\(\dfrac{17}{6}-\left(x+\dfrac{7}{6}\right)=\dfrac{7}{4}\\ \Rightarrow\dfrac{17}{6}-x-\dfrac{7}{6}=\dfrac{7}{4}\\ \Rightarrow\dfrac{5}{3}-x=\dfrac{7}{4}\\ \Rightarrow x=\dfrac{5}{3}-\dfrac{7}{4}\\ \Rightarrow x=-\dfrac{1}{12}\)

\(\left(\dfrac{1}{2}-\dfrac{1}{3}\right)-\left(\dfrac{5}{3}-\dfrac{3}{2}\right)+\left(\dfrac{7}{3}-\dfrac{5}{2}\right)\\ =\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{5}{3}+\dfrac{3}{2}+\dfrac{7}{3}-\dfrac{5}{2}\\ =\left(\dfrac{1}{2}+\dfrac{3}{2}-\dfrac{5}{2}\right)+\left(-\dfrac{1}{3}-\dfrac{5}{3}+\dfrac{7}{3}\right)\\ =-\dfrac{1}{2}+\dfrac{1}{3}\\ =-\dfrac{1}{6}\)

a)

\(\dfrac{-7}{20}\) = \(\dfrac{4}{5}\) + \(\left(\dfrac{-23}{20}\right)\) 

b)

\(\dfrac{-7}{20}\) = \(\dfrac{-1}{5}\) + \(\left(\dfrac{-3}{20}\right)\)

Do x và y là hai đại lượng tỉ lệ nghịch nên:

\(a=xy=2\cdot\left(-15\right)=-30\)