\(\Leftrightarrow36\left(x+6\right)+36\left(x-6\right)=\dfrac{9}{2}\left(x^2-36\right)\)

\(\Leftrightarrow x^2\cdot\dfrac{9}{2}-162-72x=0\)

\(\Leftrightarrow9x^2-144x-324=0\)

\(\Leftrightarrow x^2-16x-36=0\)

=>(x-18)(x+2)=0

=>x=18 hoặc x=-2

ĐKXĐ:\(x\ne\pm6\)

\(\dfrac{36}{x-6}+\dfrac{36}{x+6}=4,5\\ \Leftrightarrow36\left(\dfrac{1}{x-6}+\dfrac{1}{x+6}\right)=4,5\\ \Leftrightarrow\dfrac{x+6}{\left(x-6\right)\left(x+6\right)}+\dfrac{x-6}{\left(x-6\right)\left(x+6\right)}=\dfrac{1}{8}\\ \Leftrightarrow\dfrac{x+6+x-6}{x^2-36}=\dfrac{1}{8}\\ \Leftrightarrow\dfrac{2x}{x^2-36}=\dfrac{1}{8}\\ \Leftrightarrow x^2-36=16x\\ \Leftrightarrow x^2-16x-36=0\\ \Leftrightarrow\left(x^2+2x\right)-\left(18x+36\right)=0\\ \Leftrightarrow x\left(x+2\right)-18\left(x+2\right)=0\\ \Leftrightarrow\left(x+2\right)\left(x-18\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\left(tm\right)\\x=18\left(tm\right)\end{matrix}\right.\)

\(\dfrac{36}{x+6}+\dfrac{36}{x-6}=4,5\)

\(\Leftrightarrow36\left(x-6\right)+36\left(x+6\right)=4,5\left(x^2-36\right)\)

\(\Leftrightarrow36x-216+36x+216=4,5x^2-162\)

\(\Leftrightarrow-4,5x^2+72x+162=0\)

\(\Leftrightarrow\left(x-18\right)\left(-4,5x-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=18\\x=-2\end{matrix}\right.\)

https://olm.vn/thanhvien/chibiverycute là con chó

\(\frac{36\left(x-6\right)2}{\left(x^2-36\right)2}+\frac{36\left(x+6\right).2}{\left(x^2-36\right)2}=\frac{9\left(x^2-36\right)}{2\left(x^2-36\right)}\)

=>\(\frac{-432+72x}{\left(x^2-36\right)2}+\frac{432+72x}{\left(x^2-36\right)2}=\frac{-324+9x^2}{2\left(x^2-36\right)}\)

=>\(-432+72x+432+72x=-324+9x^2\)

=>\(-9x^2+144x+324=0=>\left(x-18\right)\left(x+2\right)=0\)

=>\(\left\{\begin{matrix}x-18=0\\x+2=0\end{matrix}\right.\)=>\(\left\{\begin{matrix}x=18\\x=-2\end{matrix}\right.\)

Vậy tập nghiệm của phương trình là S={-2;18}

2) đặt \(x^2+x+1=t\left(t>0\right)\)   ==> \(x^2+x+2=t+1\)

nên pt trên trở thành 

\(\left(\frac{1}{t}\right)^2+\left(\frac{1}{t+1}\right)^2=\frac{13}{36}\)

<=> \(\frac{1}{t^2}+\frac{1}{t^2+2t+1}=\frac{13}{36}\)

<=> \(13t^4+26t^3-59t^2-72t-36=0\)

<=> \(13t^4-26t^3+52t^3-104t^2+45t^2-90t+18t-36=0\)

<=> \(13t^3\left(t-2\right)+52t^2\left(t-2\right)+45t\left(t-2\right)+18\left(t-2\right)=0\)

<=>\(\left(t-2\right)\left(13t^3+52t^2+45t+18\right)=0\)

<=> \(\left(t-2\right)\left(t+3\right)\left(13t^2+13t+6\right)=0\)

<=> \(\orbr{\begin{cases}t=2\left(tmdk\right)\\t=-3\left(ktmdk\right)\end{cases}}\)

đến đây bạn thay vào làm nốt nhá

1.

Đặt \(a=\frac{x\left(5-x\right)}{x+1};b=x+\frac{5-x}{x+1}\)

Ta cần giải pt : \(a.b=6\)(1)

Ta có: \(a+b=\frac{x\left(5-x\right)}{x+1}+x+\frac{5-x}{x+1}=\frac{5x-x^2+x^2+x+5-x}{x+1}=5\)

\(\Rightarrow a=5-b\)

Thế \(a=5-b\)vào (1)

\(\Rightarrow\left(5-b\right)b=6\)

\(\Leftrightarrow b^2-5b+6=0\)

\(\Leftrightarrow\left(b-2\right)\left(b-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}b=2\\b=3\end{cases}\Leftrightarrow\orbr{\begin{cases}x+\frac{5-x}{x+1}=2\\x+\frac{5-x}{x+1}=3\end{cases}}}\)

Giải 2 pt trên, ta có nghiệm : \(x=1\)

\(\frac{x-90}{10}+\frac{x-76}{12}+\frac{x-58}{14}+\frac{x-36}{16}+\frac{x-15}{17}=15\)

\(\Leftrightarrow\frac{x-90}{10}-1+\frac{x-76}{12}-2+\frac{x-58}{14}-3+\frac{x-36}{16}-4+\frac{x-15}{17}-5=0\)

\(\Leftrightarrow\frac{x-100}{10}+\frac{x-100}{12}+\frac{x-100}{14}+\frac{x-100}{16}+\frac{x-100}{17}=0\)

\(\Leftrightarrow\left(x-100\right)\left(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\right)=0\)

có : \(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\ne0\)

\(\Leftrightarrow x-100=0\)

\(\Leftrightarrow x=100\)

\(pt\)\(\Leftrightarrow\)\(({x-90\over10}-1)+({x-76\over12}-2)+\)\(+({x-58\over14}-3)+({x-36\over16}-4)+({x-15\over17}-5)=0\)

\(\Leftrightarrow\)\(({x-100\over10})+({x-100\over12})+({x-100\over14})+({x-100\over16})\)

\(+({x-100\over17})=0\)

\(\Leftrightarrow\)\((x-100)({1\over10}+{1\over12}+{1\over14}+{1\over16}+{1\over17})=0\)

\(\Rightarrow\)\(x-100=0\)

\(\Rightarrow\)\(x=100\)

quy đồng xong khử mẫu là okeee 

Gợi ý :

Bài 1 : Cộng thêm 1 vào 3 phân thức đầu, trừ cho 3 ở phân thức thứ 4, có nhân tử chung là (x+2020)

Bài 2 : Trừ mỗi phân thức cho 1, chuyển vế và có nhân tử chung là (x-2021)

Bài 3 : Phân thức thứ nhất trừ đi 1, phân thức hai trù đi 2, phân thức ba trừ đi 3, phân thức bốn trừ cho 4, phân thức 5 trừ cho 5. Có nhân tử chung là (x-100)

bài 3

\(\frac{x-90}{10}+\frac{x-76}{12}+\frac{x-58}{14}+\frac{x-36}{16}+\frac{x-15}{17}=15.\)

=>\(\frac{x-90}{10}-1+\frac{x-76}{12}-2+\frac{x-58}{14}-3+\frac{x-36}{16}-4+\frac{x-15}{17}-5=0\)

=>\(\frac{x-100}{10}+\frac{x-100}{12}+\frac{x-100}{14}+\frac{x-100}{16}+\frac{x-100}{17}=0\)

=>\(\left(x-100\right).\left(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\right)=0\)

=>(x-100)=0 do \(\frac{1}{10}+\frac{1}{12}+\frac{1}{14}+\frac{1}{16}+\frac{1}{17}\ne0\)

=> x=100

\(\frac{x+2}{2018}+\frac{x+3}{2017}+\frac{x+4}{2016}+\frac{x+2036}{6}=0\)

\(\Leftrightarrow\frac{x+2}{2018}+1+\frac{x+3}{2017}+1+\frac{x+4}{2016}+1+\frac{x+2038}{6}-3=0\)

\(\Leftrightarrow\frac{x+2020}{2018}+\frac{x+2020}{2017}+\frac{x+2020}{2016}+\frac{x+2020}{6}=0\)

\(\Leftrightarrow\left(x+2020\right)\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{6}\right)=0\)

có : \(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}+\frac{1}{6}\ne0\)

\(\Leftrightarrow x+2020=0\)

\(\Leftrightarrow x=-2020\)

\(\frac{x-3}{2018}+\frac{x-2}{2019}=\frac{x-2019}{2}+\frac{x-2018}{3}\)

\(\Leftrightarrow\frac{x-3}{2018}-1+\frac{x-2}{2019}-1=\frac{x-2019}{2}-1+\frac{x-2018}{3}-1\)

\(\Leftrightarrow\frac{x-2021}{2018}+\frac{x-2021}{2019}=\frac{x-2021}{2}+\frac{x-2021}{3}\)

bài 3 thì lần lượt trừ đi 1; 2; 3; 4; 5