\(\frac{60}{x}=\frac{30}{x-6}+\frac{30}{x+10}\)

\(\Leftrightarrow\frac{60}{x}=\frac{30}{x-6}+\frac{30}{x+10},Đkxđ:x\ne0,6,-10\)

\(\Leftrightarrow\frac{60}{x}-\frac{30}{x-6}-\frac{30}{x+10}=0\)

\(\Leftrightarrow\frac{60\left(x-6\right)\left(x+10\right)-30x\left(x+10\right)=30\left(x-6\right)}{x\left(x-6\right)\left(x+10\right)}\)

\(\Leftrightarrow\frac{\left(60x-360\right)\left(x+10\right)-30x^2-300x-30x^2+180x}{x\left(x-6\right)\left(x+10\right)}\)

\(\Leftrightarrow\frac{60x^2+600x-360x-3600-30x^2-300x-30x^2+180}{x\left(x-6\right)\left(x=10\right)}=0\)

\(\Leftrightarrow\frac{120x-3600}{x\left(x-6\right)\left(x+10\right)}=0\)

\(\Leftrightarrow120x-3600=0\)

\(\Leftrightarrow120x=3600\)

\(\Leftrightarrow x=30;x\ne0;x\ne6,x\ne-10\)

Từ đề bài, ta có:

\(2+\frac{x-30}{10}+2+\frac{x-28}{9}+2+\frac{x-26}{8}=0\)

\(\Leftrightarrow\frac{x-10}{10}+\frac{x-10}{9}+\frac{x-10}{8}=0\)

\(\Leftrightarrow\left(x-10\right)\left(\frac{1}{10}+\frac{1}{9}+\frac{1}{8}\right)=0\)

Do \(\left(\frac{1}{10}+\frac{1}{9}+\frac{1}{8}\right)>0\)nên x-10=0

<=> x=10

Vậy phương trình có nghiệm duy nhất x=10

@Gà Mờ Thks bạn 

pt <=> 1/(x+2).(x+3) + 1/(x+3).(x+4) + 1/(x+4).(x+5) + 1/(x+5).(x+6) = 1/8

<=> 1/x+2 - 1/x+3 + 1/x+3 - 1/x+4 + 1/x+4 - 1/x+5 + 1/x+5 - 1/x+6 = 1/8

<=> 1/x+2 - 1/x+6 = 1/8

<=> (x+6-x-2)/(x+2).(x+6) = 1/8

<=> 4/(x+2).(x+6) = 1/8

<=>(x+2).(x+6) = 4 : 1/8 = 32

<=>x^2 + 8x + 12 = 32

<=> x^2+8x+12-32=0

<=>x^2+8x-20=0

<=>(x-2).(x+10)=0

<=> x-2 =0 hoặc x+10 = 0

<=> x=2 hoặc x=-10

giang sinh an lanh $%###Xuyen gam cu chuoi###%$

\(\frac{x-30}{10}+\frac{x-28}{9}+\frac{x-26}{8}=-6\)

<=> \(\frac{36.\left(x-30\right)}{360}+\frac{40\left(x-28\right)}{360}+\frac{45\left(x-26\right)}{360}=\frac{-2160}{360}\)

=> \(36x-1080+40x-1120+45x-1170=-2160\)

\(< =>36x+40x+45x=-2160+1080+1120+1170\)

<=> \(121x=1210\)

<=> x = 10

ok

Bạn có thể làm bằng cách khác đc ko

hiu hiu

help me !!!!

ko biết ok

hk biết

phân tích mẫu thành nhân tử r` tách ra rút gọn như kiểu bài tính của lớp 5 ấy

bài tương tự : Câu hỏi của Lê Phương Oanh - Toán lớp 8 | Học trực tuyến (https://h-o-c-24.vn/hoi-dap/question/179719.html)

\(a)\;sinx = \frac{{\sqrt 3 }}{2}\)

Vì \(sin\frac{\pi }{3} = \frac{{\sqrt 3 }}{2}\) nên \(sinx = \frac{{\sqrt 3 }}{2} \Leftrightarrow sin\frac{\pi }{3} = sin\frac{\pi }{3}\) \( \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{3} + k2\pi ,k \in \mathbb{Z}\\x = \pi  - \frac{\pi }{3} + k2\pi ,k \in \mathbb{Z}\end{array} \right.\)

\( \Leftrightarrow \left[ \begin{array}{l}x = \frac{\pi }{3} + k2\pi ,k \in \mathbb{Z}\\x = \frac{{2\pi }}{3} + k2\pi ,k \in \mathbb{Z}\end{array} \right.\)

Vậy phương trình có nghiệm là \(x = \frac{\pi }{3} + k2\pi \) hoặc \(x = \frac{{2\pi }}{3} + k2\pi \)\(,k \in \mathbb{Z}\).

\(\begin{array}{l}b)\;sin(x + {30^o}) = sin(x + {60^o})\\ \Leftrightarrow \left[ \begin{array}{l}x + {30^o} = x + {60^o} + k{360^o},k \in \mathbb{Z}\\x + {30^o} = {180^o} - x - {60^o} + k{360^o},k \in \mathbb{Z}\end{array} \right.\\ \Leftrightarrow x = {45^o} + k{180^o},k \in \mathbb{Z}.\end{array}\)

Vậy phương trình có nghiệm là \(x = {45^o} + k{180^o},k \in \mathbb{Z}\).

\(\frac{x-15}{2014}+\frac{x-20}{2019}=\frac{x-5}{2004}+\frac{x+30}{1969}\)

\(\Leftrightarrow\frac{x-15}{2014}+1+\frac{x-20}{2019}+1=\frac{x-5}{2004}+1+\frac{x+30}{1969}+1\)

\(\Leftrightarrow\frac{x-15+2014}{2014}+\frac{x-20+2019}{2019}-\frac{x-5+2004}{2004}-\frac{x+30+1969}{1969}=0\)

\(\Leftrightarrow\frac{x-1999}{2014}+\frac{x+1999}{2019}-\frac{x+1999}{2004}-\frac{x+1999}{1969}=0\)

\(\Leftrightarrow\left(x-1999\right)\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)=0\)

Vì \(\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)\ne0\)

nên \(x-1999=0\)

\(\Leftrightarrow x=1999\)

\(easy!\)(sai đề + sửa đề)

\(\frac{x-5}{2014}+\frac{x-20}{2019}-\frac{x-5}{2004}-\frac{x+3}{1969}=0\)

\(\Leftrightarrow\left(\frac{x-15}{2014}-1\right)+\left(\frac{x-20}{2019}-1\right)-\left(\frac{x-5}{2004}-1\right)-\left(\frac{x-30}{1969}-1\right)=0\)

\(\Leftrightarrow\frac{x-1999}{2014}+\frac{x-1999}{2019}-\frac{x-1999}{2004}-\frac{x-1999}{1969}=0\)

\(\Leftrightarrow\left(x-1999\right)\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)=0\)

dễ dàng cm được \(x-1999=0\)

\(\Leftrightarrow x=1999\)

          \(\frac{x+1999}{2014}-1+\frac{x+1999}{2019}-1=\frac{x+1999}{2004}-1+\frac{x+1999}{1969}\)

<=>   \(\frac{x+1999}{2014}+\frac{x+1999}{2019}-\frac{x+1999}{2004}-\frac{x+1999}{1969}=0\)

<=> \(\left(x+1999\right)\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)=0\)

 Vì     \(\frac{1}{2014}+\frac{1}{2014}-\frac{1}{2004}-\frac{1}{1969}\)khác 0 (tự c/m)

  => x+1999=0

  => x=-1999

     Vậy x=-1999 thì ......