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

a) 3x² + 3x - 6 = 3(x² + x - 2) = 3(x² - x + 2x - 2) = 3[x(x - 1) + 2(x - 1)] = 3(x - 1)(x + 2)

b) 3x² - 3x - 6 = 3(x² - x - 2) = 3(x² + x - 2x - 2) = 3[x(x + 1) - 2(x + 1)] = 3(x + 1)(x - 2)

D

d

D

 (3x - 6)^4 = (3x-6)^6

=> (3x-6)^6 - (3x-6)^4 = 0

=> (3x-6)^4 . [ (3x-6)^2 - 1] = 0

=> (3x-6)^4 = 0 hoặc (3x-6)^2 = 1

=> 3x - 6 = 0 hoặc 3x - 6 = 1 hoặc 3x - 6 = -1

=> x = 2 hoặc x = 7/3 hoặc x = 5/3

b, (3\(x\) - 6)⁴ = (3\(x\) - 6)⁶

    (3\(x\) - 6)⁶ - (3\(x\)  - 6)⁴ = 0

    (3\(x\) - 6)⁴.[(3\(x\) - 6)² - 1) = 0

     \(\left[{}\begin{matrix}3x-6=0\\3x-6=\pm1\end{matrix}\right.\)

     \(\left[{}\begin{matrix}x=2\\x=\dfrac{7}{3}\\x=\dfrac{5}{3}\end{matrix}\right.\)

sao đề nhìn bá vậy bạn ...

bài này chắc đặt \(\sqrt{x^3-3x+6}\)cho nó gọn thôi

B. 3x-6

Lời giải:
ĐK: $x\geq \frac{1}{3}$

PT $\Leftrightarrow \sqrt{(3x-1)+6\sqrt{3x-1}+9}+\sqrt{(3x-1)-6\sqrt{3x-1}+9}=3x+4$
$\Leftrightarrow \sqrt{(\sqrt{3x-1}+3)^2}+\sqrt{(\sqrt{3x-1}-3)^2}=3x+4$

$\Leftrightarrow |\sqrt{3x-1}+3|+|\sqrt{3x-1}-3|=3x+4$

Nếu $x\geq \frac{10}{3}$ thì:

$\sqrt{3x-1}+3+\sqrt{3x-1}-3=3x+4$

$\Leftrightarrow 2\sqrt{3x-1}=3x+4$

$\Leftrightarrow 2\sqrt{3x-1}=(3x-1)+5$

$\Leftrightarrow (\sqrt{3x-1}-1)^2=-4< 0$ (vô lý)

Nếu $\frac{1}{3}\leq x< \frac{10}{3}$ thì:

$\sqrt{3x-1}+3+3-\sqrt{3x-1}=3x+4$

$\Leftrightarrow 2=3x\Leftrightarrow x=\frac{2}{3}$ (thỏa mãn)

Vậy.......

\(a,\frac{7}{3}x+5=\frac{9}{6}x-7\)

\(\frac{7}{3}x-\frac{9}{6}x=-7-5\)

  \(\left(\frac{7}{3}-\frac{9}{6}\right).x=-12\)

                  \(\frac{5}{6}.x=-12\)

                        \(x=\left(-12\right):\frac{5}{6}\)

                        \(x=-\frac{72}{5}\)

\(b,3x+\frac{6}{4}=5-\frac{7x}{6}\)

\(3x+\frac{7x}{6}=5-\frac{6}{4}\)

\(\left(3+\frac{7}{6}\right).x=\frac{7}{2}\)

\(\frac{25}{6}.x=\frac{7}{2}\)

\(x=\frac{7}{2}:\frac{25}{6}\)

\(x=\frac{21}{25}\)

\(c,\frac{12}{5}x+6=\frac{17}{3}x+12\)

\(\frac{12}{5}x-\frac{17}{3}x=12-6\)

            \(-\frac{49}{15}x=6\)

                       \(x=6:\left(-\frac{49}{15}\right)\)

                       \(x=-\frac{90}{49}\)

\(d,6\left(3x+7\right)=12\left(2x-4\right)\)

       \(18x+42=24x-48\)

     \(18x-24x=-48-42\)

                 \(-6x=-90\)

                        \(x=15\)

\(e,13\left(2x-9\right)=8\left(3x-13\right)\)

      \(26x-117=24x-104\)

      \(26x-24x=-104+117\)

                      \(2x=13\)

                        \(x=\frac{13}{2}\)