Bài 7: Phép cộng phân số

`(-3/4)+(-1/4)+2/7+5/7+3/5`

`=[(-3/4)+(-1/4)]+(2/7+5/7)+3/5`

`=-4/4+7/7+3/5`

`=-1+1+3/5`

`=0+3/5`

`=3/5`

-3/4 + -1/4 + 2/7  + 5/7 + 3/5 

= (-3/4 + -1/4) + (2/7  + 5/7) + 3/5

= (-1 + 1) + 3/5

= 0 + 3/5

= 0

=-65/50-28/50=-93/50

\(\dfrac{13}{-10}+\dfrac{-14}{25}=\dfrac{-65}{50}+\dfrac{-28}{50}=\dfrac{-93}{50}\) (quy đồng mẫu số)

1/2^2<1/1*2

1/3^2<1/2*3

...

1/9^2<1/8*9

=>A<1-1/2+1/2-1/3+...+1/8-1/9=8/9

1/2^2>1/2*3

1/3^2>1/3*4

...

1/9^2>1/9*10

=>A>1/2-1/3+1/3-1/4+...+1/9-1/10=2/5

=>2/5<A<8/9

\(-\dfrac{13}{7}+\dfrac{3}{5}+\left(-\dfrac{1}{7}\right)\)

\(=-\dfrac{13}{7}+\left(-\dfrac{1}{7}\right)+\dfrac{3}{5}\)

\(=-\dfrac{14}{7}+\dfrac{3}{5}\)

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

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

\(=-\dfrac{7}{5}\)

\(\dfrac{-13}{7}+\dfrac{3}{5}+\dfrac{-1}{7}\)

\(=\left(\dfrac{-13}{7}+\dfrac{-1}{7}\right)+\dfrac{3}{5}\)

\(=\dfrac{-13+\left(-1\right)}{7}+\dfrac{3}{5}\)

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

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

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

\(=\dfrac{-7}{5}\)

\(\dfrac{x+1}{x-3}=\dfrac{x+7}{x-2}\) ĐK : \(\left\{{}\begin{matrix}x-3\ne0\\x-2\ne0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ne3\\x\ne2\end{matrix}\right.\)

`=> (x+1)(x-2)=(x-3)(x+7)`

`=> x^2 -2x +x-2 = x^2+7x-3x-21`

`=> x^2 -x -2 = x^2+4x-21`

`=>x^2 -x-x^2-4x = -21+2`

`=> -5x = -19`

`=>x=19/5` (t/m)

\(\dfrac{3}{54}+\dfrac{5}{126}+\dfrac{7}{294}\\ =\dfrac{1}{18}+\dfrac{5}{126}+\dfrac{1}{42}\\ =\dfrac{7}{126}+\dfrac{5}{126}+\dfrac{3}{126}\\ =\dfrac{15}{126}=\dfrac{5}{42}\\ \\ \dfrac{5}{24}+\dfrac{5}{104}+\dfrac{5}{234}\\ =\dfrac{121680}{584064}+\dfrac{28080}{584064}+\dfrac{12480}{584064}\\ =\dfrac{162240}{584064}=\dfrac{5}{18}\)

\(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+...+\dfrac{1}{90}\)

\(=\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+...+\dfrac{1}{9\cdot10}\)

\(=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{9}-\dfrac{1}{10}\)

\(=\dfrac{1}{4}-\dfrac{1}{10}=\dfrac{5-2}{20}=\dfrac{3}{20}\)

40 hay 42 vậy ạ

x^2+2x+3=x^2+2x+1+2

=(x+1)^2+2>=2

Dấu = xảy ra khi x=-1

`x/(-8) = 2/(-x^3)`

`=> x.(-x^3) = 2. (-8)`

`=> -x^4 = -16`

`=> x=+-2`

x=2 , x³ = 2