Bài 7: Phép cộng phân số

`-24/17- (-7/17-1/6)`

`=-24/17+7/17+1/6`

`=-17/17+1/6`

`=-1+1/6`

`=-6/6+1/6`

`=-5/6`

\(\dfrac{-24}{17}-\left(\dfrac{-7}{17}-\dfrac{1}{6}\right)\\ =\dfrac{-24}{17}+\dfrac{7}{17}+\dfrac{1}{6}\\ =-1+\dfrac{1}{6}\\ =\dfrac{-5}{6}\)

`-24/17-(-7/17-1/6)`

`=-24/17+7/17+1/6`

`=-17/17+1/6`

`=-1+1/6`

`=-6/6+1/6`

`=-5/6`

`(-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

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\)
\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{10.11}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=1-\dfrac{1}{11}\)
\(=\dfrac{10}{11}\)

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\\ =\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{10.11}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\\ =1-\dfrac{1}{11}=\dfrac{10}{11}\)

\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\\ =\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{10.11}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\\ =1-\dfrac{1}{11}\\ =\dfrac{10}{11}\)

\(\dfrac{x+1}{x-3}=\dfrac{x+7}{x-2}\) 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)

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

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

`=> -x^4 = -16`

`=> x=+-2`

x=2 , x³ = 2

a: 58/63=3190/3465

36/55=2268/3465

=>58/63>36/55

b: 27/53=1998/3922

36/74=1908/3922

=>27/53>36/74

a: 58/63=3190/3465

36/55=2268/3465

=>58/63>36/55

b: 27/53=1998/3922

36/74=1908/3922

=>27/53>36/74

`-11/19 - ( 15/7 - 11/19) + 8/7`

`=-11/19 -15/7 + 11/19 + 8/7`

`=(-11/19 +11/19) - (15/7 -8/7)`

`=0- 1`

`=-1`

`-11/19 - (15/7 - 11/19)+8/7`

`=-11/19-15/7+11/19+8/7`

`=(-11/9+11/9)+(-15/7+8/7)`

`=0+(-7)/7`

`=0+(-1)`

`=-1`

`#iv`

`-1/2 -(x+ (-3)/8 )=1/8`

`=> x+ (-3)/8=-1/2 -1/8`

`=> x+ (-3)/8= -4/8 -1/8`

`=> x+ (-3)/8= -5/8`

`=>x= -5/8 -(-3)/8`

`=>x= -5/8+3/8`

`=>x= 2/8=1/4`

\(\dfrac{x}{3}+\dfrac{13}{18}=\dfrac{19}{18}\)

\(\dfrac{x}{3}=\dfrac{6}{18}\)

\(=>\dfrac{x}{3}=\dfrac{1}{3}\)

\(=>x=1\)

\(#PaooNqoccc\)