\(\frac{7x-12}{5x-2}=\frac{9-7x}{-5x+1}\)

\(=>\frac{2x-10}{5x-2}+1=\frac{-7x+9}{-5x+1}=\frac{-2x+8}{-5x+1}+1\)

\(=>\frac{2x-10}{5x-2}=\frac{-2x+8}{-5x+1}=\frac{-\left(2x-8\right)}{-\left(5x-1\right)}=\frac{2x-8}{5x-1}\)

\(=>\frac{2x-10}{5x-2}=\frac{2x-8}{5x-1}\)

\(=>\frac{5x-1}{5x-2}=\frac{2x-8}{2x-10}\)

\(=>\frac{-1}{5x-2}=\frac{-2}{2x-10}\)

\(=>-2x+10=-10x+4\)

\(=>-2x+10x=4-10=-6\)

\(=>8x=-6\)

\(=>x=\frac{-6}{8}=\frac{-3}{4}\)

P/s ko chắc :v

Ta có: \(\frac{7x-12}{5x-2}=\frac{7x-9}{5x-1}\)

     \(\Rightarrow\left(7x-12\right).\left(5x-1\right)=\left(7x-9\right).\left(5x-2\right)\)

    \(\Leftrightarrow35x^2-7x-60x+12=35x^2-14x-45x+18\)

    \(\Leftrightarrow\left(35x^2-35x^2\right)-\left(7x+60x-14x-45x\right)=18-12\)

    \(\Leftrightarrow8x=6\)

    \(\Leftrightarrow x=\frac{3}{4}\)

Vậy \(\Leftrightarrow x=\frac{3}{4}\)

\(\frac{7x-12}{5x-2}=\frac{9-7x}{-5x+1}\)

\(\left(7x-12\right)\left(-5x+1\right)=\left(9-7x\right)\left(5x-2\right)\)

\(-35x^2+7x+60x-12=45x-18-35x^2+14x\)

\(67x-12=59x-18\)

\(67x-12-59x=18\)

\(8x-12=-18\)

\(8x=-18+12\)

\(8x=-6\)

\(x=-\frac{6}{8}=-\frac{3}{4}\)

3: \(\Leftrightarrow a-15=0\)

hay a=15

*) (-7) - (-12) + (-5)

= [(-7) + (-5)] + 12

= (-12) + 12

= 0

*) (-2) . 3² + 7 . (-4) - (-34)

= (-2) . 9 + (-28) + 34

= -18 + (-28) + 34

= -46 + 34

= -12

*) 12 . (-82) + (-12).18

= (-12) . 82 + (-12) . 18

= (-12) . (82 + 18)

= (-12) . 100

= -1200

( - 7 )- ( - 12 ) + ( - 5) = 0
( - 2 ) x 3²+ 7 . (-4) - ( -34) = - 970
12 x ( -82 ) + (-12) x18  = - 1200

( - 7 )- ( - 12 ) + ( - 5)
= (-7) + 12 + (-5)
= 5 + (-5)
= 0
(- 2) x 3²+ 7 . (-4) - ( -34)
= (-2) x 9 + 7 x (-4) - (-34)
= -18 + (-28) - (-34)
= -18 + (-28) + 34
= -46 + 34
= -12
12 x ( -82 ) + (-12) x18
= -984 + (-216)
= -1200

a) \(5x^2-7x-12=0\)

Ta có: \(a=5;b=-7;c=-12\)

\(\Rightarrow\Delta=b^2-4ac=\left(-7\right)^2-4.5.\left(-12\right)=289\)

Vậy phương trình có 2 nghiệm:

\(\left\{{}\begin{matrix}x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-\left(-7\right)-\sqrt{289}}{2.5}=-1\\x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-\left(-7\right)+\sqrt{289}}{2.5}=2,4\end{matrix}\right.\)

a)x²-5x+6=(x²-2x)-(3x-6)=x(x-2)-3(x-2)(=(x-2)(x-3)

b)x²+5x+6=(x²+2x)+(3x+6)=x(x+2)+3(x+2)=(x+2)(x+3)

c)x²-7x+12=(x²-3x)-(4x-12)=x(x-3)-4(x-3)=(x-3)(x-4)

d)x²+7x+12=(x²+3x)+(4x+12)=x(x+3)+4(x+3)=(x+3)(x+4)

a: \(\dfrac{x^2-5x+6}{x^2+7x+12}:\dfrac{x^2-4x+4}{x^2+3x}\)

\(=\dfrac{\left(x-2\right)\left(x-3\right)}{\left(x+3\right)\left(x+4\right)}\cdot\dfrac{x\left(x+3\right)}{\left(x-2\right)^2}\)

\(=\dfrac{x\left(x-3\right)}{\left(x-2\right)\left(x+4\right)}\)

b: \(\dfrac{x^2+2x-3}{x^2+3x-10}:\dfrac{x^2+7x+12}{x^2-9x+14}\)

\(=\dfrac{\left(x+3\right)\left(x-1\right)}{\left(x+5\right)\left(x-2\right)}\cdot\dfrac{\left(x-2\right)\left(x-7\right)}{\left(x+3\right)\left(x+4\right)}\)

\(=\dfrac{\left(x-1\right)\left(x-7\right)}{\left(x+5\right)\left(x+4\right)}\)

1) x² -7x + 10 = x² - 2x - 5x + 10 = x(x - 2) - 5(x - 2) = (x - 5)(x - 2)

2) x² + 3x + 2 = x² + 2x + x  + 2 = x(x + 2) + (x + 2) = (x + 1)(x + 2)

3) x² - 7x + 12 = x² - 3x - 4x + 12 = x(x - 3) - 4(x - 3) = (x - 3)(x - 4)

4) x² + 7x + 12 = x² + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 3)(x + 4)

5) 16x - 5x² - 3 = 15x - 5x² + x - 3 = -5x(x - 3) + (x - 3) = (x - 3)(1 - 5x) 

6) 6x² + 7x - 3 = 6x² - 2x + 9x - 3 = 2x(3x - 1) + 3(3x - 1) = (2x + 3)(3x - 1)  

7) 3x² - 3x - 6 = 3x² - 6x + 3x - 6 = 3x(x - 2) + 3(x - 2) = (x - 2)(3x + 3) = 3(x - 2)(x + 1)

8) 3x² + 3x - 6 = 3x² - 3x + 6x - 6 = 3x(x - 1) + 6(x - 1) = (x - 1)(3x + 6) = 3(x - 1)(x + 2)

9) 6x² - 13x + 6 = 6x² - 9x -  4x + 6 = 3x(2x - 3) - 2(2x - 3) = (3x - 2)(2x - 3) 

10) 6x² + 15x  + 6 = 6x² + 12x + 3x + 6 = 6x(x + 2) + 3(x + 2) = (x + 2)(6x + 3) = 3(x + 2)(3x + 1)

11) 6x² - 20x + 6 = 6x² - 18x - 2x + 6 = 6x(x -3) - 2(x - 3) = (6x - 2)(x - 3) = 2(3x - 1)(x - 3)

12) 8x² + 5x - 3 = 8x² + 8x - 3x - 3 = 8x(x + 1) - 3(x + 1) = (x + 1)(8x - 3)

\(\left(7x-19\right)-\left(5x-12\right)=3x-\left(9-2x\right)-1\)

\(\Leftrightarrow7x-19-5x+12=3x-9+2x-1\)

\(\Leftrightarrow-3x=3\)

\(\Leftrightarrow x=-1\)