\(\frac{1}{y\left(y+1\right)}\) + \(\frac{1}{\left(y+1\right)\left(y+2\right)}\) + \(\frac{1}{\left(y+2\right)\left(y+3\right)}\) + \(\frac{1}{\left(y+3\right)\left(y+4\right)}\)= \(\frac{1}{15}\)

\(\frac{1}{y}\) - \(\frac{1}{y+1}\) + \(\frac{1}{y+1}\) - \(\frac{1}{y+2}\) + \(\frac{1}{y+2}\) - \(\frac{1}{y+3}\) + \(\frac{1}{y+3}\) - \(\frac{1}{y+4}\) = \(\frac{1}{15}\) 

\(\frac{1}{y}\) + \(\frac{1}{y+1}\) - \(\frac{1}{y+1}\) + \(\frac{1}{y+2}\) - \(\frac{1}{y+2}\) + \(\frac{1}{y+3}\) - \(\frac{1}{y+3}\) - \(\frac{1}{y+4}\) = \(\frac{1}{15}\)

\(\frac{1}{y}\) - \(\frac{1}{y+4}\) = \(\frac{1}{15}\)

\(\frac{4}{y\left(y+4\right)}\) = \(\frac{1}{15}\) => \(\frac{4}{y\left(y+4\right)}\)= \(\frac{4}{60}\)

=> y(y+4)=60 Mà 60 = 1.60=2.30=3.20=4.15=5.12=6.10

Vậy y(y+4)=6.10 => y=6. Vậy y=6

2: Tọa độ giao điểm là:

\(\left\{{}\begin{matrix}2x-1=x+1\\y=x+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)

a) \(y+2\frac{1}{3}=3\)

=> y + 7/3 = 3

=> y = 3 - 7/3

=> y = 2/3

b) \(y-1\frac{1}{4}=1\frac{1}{8}\)

=> y - 5/4 = 9/8

=> y = 9/8 + 5/4

=> y = 19/8

c) \(3-y=1\frac{1}{4}\)

=> 3 - y = 5/4

=> y =  3  - 5/4

=> y = 7/4

d) \(y\times2\frac{3}{5}=1\frac{13}{15}\)

=> y x 13/5 = 28/15

=> y = 28/15 : 13/5

=> y = 28/39

e) \(2:y=2\frac{3}{7}\)

=> 3 : y = 17/7

=> y = 3 : 17/7

=> y = 21/17

a) y + 2/1/3 = 3

y + 7/3 = 3

y = 2/3

cac bai con lai bn tu dua vao cong thuc da hoc mak lm nha!

a) y + 2/1/3 = 3

y + 7/3 = 3

y = 2/3

cac bai con lai bn tu dua vao cong thuc da hoc mak lm nha!

Bài 1: 

c) \(\dfrac{1}{y}\sqrt{19y}=\sqrt{19y\cdot\dfrac{1}{y^2}}=\sqrt{\dfrac{19}{y}}\)

d) \(\dfrac{1}{3y}\cdot\sqrt{\dfrac{27}{y^2}}\cdot y=\sqrt{\dfrac{1}{9}\cdot\dfrac{27}{y^2}}=\sqrt{\dfrac{3}{y^2}}\)

Bài 3: 

a) Ta có: \(\left(\dfrac{2}{\sqrt{3}-1}+\dfrac{3}{\sqrt{3}-2}+\dfrac{15}{3-\sqrt{3}}\right)\cdot\dfrac{1}{\sqrt{3}+5}\)

\(=\left(\dfrac{2\left(\sqrt{3}+1\right)}{2}-\dfrac{3\left(2+\sqrt{3}\right)}{1}+\dfrac{15\left(3+\sqrt{3}\right)}{6}\right)\cdot\dfrac{1}{\sqrt{3}+5}\)

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

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

\(=\dfrac{-2+15+5\sqrt{3}}{2\left(5+\sqrt{3}\right)}\)

\(=\dfrac{13+5\sqrt{3}}{10+2\sqrt{3}}\)

`a)TXĐ: R`

`b)TXĐ: R\\{0}`

`c)TXĐ: R\\{1}`

`d)TXĐ: (-oo;-1)uu(1;+oo)`

`e)TXĐ: (-oo;-1/2)uu(1/2;+oo)`

`f)TXĐ: (-oo;-\sqrt{2})uu(\sqrt{2};+oo)`

`h)TXĐ: (-oo;0) uu(2;+oo)`

`k)TXĐ: R\\{1/2}`

`l)ĐK: {(x^2-1 > 0),(x-2 > 0),(x-1 ne 0):}`

`<=>{([(x > 1),(x < -1):}),(x > 2),(x ne 1):}`

`<=>x > 2`

   `=>TXĐ: (2;+oo)`

Giải:

a) \(\dfrac{-5}{8}=\dfrac{x}{16}\) 

\(\Rightarrow x=\dfrac{16.-5}{8}=-10\) 

\(\dfrac{3x}{9}=\dfrac{2}{6}\) 

\(\Rightarrow3x=\dfrac{2.9}{6}=3\) 

\(\Rightarrow x=1\)

b) \(\dfrac{x+3}{15}=\dfrac{1}{3}\)  

\(\Rightarrow x+3=\dfrac{1.15}{3}=5\) 

\(\Rightarrow x=2\)

\(\dfrac{6}{2x+1}=\dfrac{2}{7}\) 

\(\Rightarrow2x+1=\dfrac{6.7}{2}=21\) 

\(\Rightarrow x=10\)

c) \(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\) 

\(\Rightarrow\dfrac{4}{x-6}=\dfrac{-12}{18}\) 

\(\Rightarrow x-6=\dfrac{18.4}{-12}=-6\) 

\(\Rightarrow x=0\) 

\(\Rightarrow\dfrac{y}{24}=\dfrac{-12}{18}\) 

\(\Rightarrow y=\dfrac{-12.24}{18}=-16\) 

 \(\dfrac{3-x}{-12}=\dfrac{16}{y+1}=\dfrac{192}{-72}\) 

\(\Rightarrow\dfrac{3-x}{-12}=\dfrac{192}{-72}\) 

\(\Rightarrow3-x=\dfrac{192.-12}{-72}=32\) 

\(\Rightarrow x=-29\) 

\(\Rightarrow\dfrac{16}{y+1}=\dfrac{192}{-72}\) 

\(\Rightarrow y+1=\dfrac{16.-72}{192}=-6\) 

d) \(\dfrac{-2}{3}< \dfrac{x}{5}< \dfrac{-1}{6}\) 

\(\Rightarrow\dfrac{-20}{30}< \dfrac{6x}{30}< \dfrac{-5}{30}\) 

\(\Rightarrow6x\in\left\{-18;-12;-6\right\}\) 

\(\Rightarrow x\in\left\{-3;-2;-1\right\}\) 

\(\dfrac{-1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\) 

\(\Rightarrow\dfrac{-8}{40}\le\dfrac{5x}{40}\le\dfrac{10}{40}\) 

\(\Rightarrow5x\in\left\{-5;0;5;10\right\}\) 

\(\Rightarrow x\in\left\{-1;0;1;2\right\}\) 

e) \(\dfrac{x+46}{20}=x\dfrac{2}{5}\) 

\(\Rightarrow\dfrac{x+46}{20}=x+\dfrac{2}{5}\) 

\(\Rightarrow\dfrac{x+46}{20}=\dfrac{5x+2}{5}\) 

\(\Rightarrow5.\left(x+46\right)=20.\left(5x+2\right)\) 

\(\Rightarrow5x+230=100x+40\) 

\(\Rightarrow5x-100x=40-230\) 

\(\Rightarrow-95x=-190\) 

\(\Rightarrow x=-190:-95\) 

\(\Rightarrow x=2\) 

\(y\dfrac{5}{y}=\dfrac{86}{y}\) 

\(\Rightarrow y+\dfrac{5}{y}=\dfrac{86}{y}\) 

\(\Rightarrow\dfrac{y^2+5}{y}=\dfrac{86}{y}\) 

\(\Rightarrow y^2+5=86\) 

\(\Rightarrow y^2=86-5\) 

\(\Rightarrow y^2=81\) 

\(\Rightarrow\left[{}\begin{matrix}y=9\\y=-9\end{matrix}\right.\) 

Chúc bạn học tốt!