\(\dfrac{7m+4}{3m+3}\ge0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}7m+4\ge0\\3m+3>0\end{matrix}\right.\\\left\{{}\begin{matrix}7m+4< 0\\3m+3< 0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m\ge-\dfrac{4}{7}\\m>-1\end{matrix}\right.\\\left\{{}\begin{matrix}m< -\dfrac{4}{7}\\m< -1\end{matrix}\right.\end{matrix}\right.\) (khi kết hợp mấy cái này, trường hợp bất đẳng thức CÙNG CHIỀU, thì LỚN HƠN THÌ LẤY LỚN HƠN, BÉ HƠN THÌ LẤY BÉ HƠN)

\(\Leftrightarrow\left[{}\begin{matrix}m\ge-\dfrac{4}{7}\\m< -1\end{matrix}\right.\) (xong! )

Kl: Vậy \(\left[{}\begin{matrix}m\ge-\dfrac{4}{7}\\m< -1\end{matrix}\right.\)

Đk: x >/ 5

pt đã cho \(\Leftrightarrow7\sqrt{x-2}-14\cdot\dfrac{\sqrt{x-2}}{7}-3\sqrt{x-5}=4\)

\(\Leftrightarrow7\sqrt{x-2}-2\sqrt{x-2}-3\sqrt{x-5}=4\)

\(\Leftrightarrow5\sqrt{x-2}-3\sqrt{x-5}=4\)

\(\Leftrightarrow5\sqrt{x-2}=4+3\sqrt{x-5}\)

\(\Leftrightarrow25x-50=16+9x-45+24\sqrt{x-5}\)

\(\Leftrightarrow16x-21=24\sqrt{x-5}\)

\(\Leftrightarrow\left\{{}\begin{matrix}256x^2-672x+441=576x-2880\\x\ge\dfrac{21}{16}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}256x^2-1248x+3321=0\\x\ge\dfrac{21}{16}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}256x^2-1248x+3321=0\left(vn\right)\\x\ge\dfrac{21}{16}\end{matrix}\right.\)

Kl: ptvn

a) \(3x-3y+6xy+6y^2=3\left(x-y+2xy+2y^2\right)\)

b) \(4x^2-8xy-4z^2+4y^2=4\left(x^2-2xy+y^2-z^2\right)=4\left(\left(x-y\right)^2-z^2\right)=4\left(x-y-z\right)\left(x-y+z\right)\)

c) \(125a^3-8=\left(5a-2\right)\left(25a^2+10a+4\right)\)

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

e) \(a^2b+ab^2+a^3+b^3=ab\left(a+b\right)+\left(a+b\right)\left(a^2-ab+b^2\right)=\left(a+b\right)\left(a^2+b^2\right)\)

\(\left(\dfrac{x^2}{y^2}+\dfrac{x}{y}\right):\left(\dfrac{x}{y^2}-\dfrac{1}{y}+\dfrac{1}{x}\right)=\left(\dfrac{x^2}{y^2}+\dfrac{xy}{y^2}\right):\left(\dfrac{x^2}{xy^2}-\dfrac{xy}{xy^2}+\dfrac{y^2}{xy^2}\right)\)

đến đây thôi