Sửa đề \(D=\frac{a^3+3^3}{b^3+4^3}\)biết \(\frac{a+3}{a-3}=\frac{b+4}{b-4}\)

\(\Leftrightarrow\left(a+3\right)\left(b-4\right)=\left(a-3\right)\left(b+4\right)\)

\(\Leftrightarrow ab-4a+3b-12=ab+4a-3b-12\)

\(\Leftrightarrow8a=6b\)

\(\Leftrightarrow\frac{a}{6}=\frac{b}{8}\Leftrightarrow\frac{a}{3}=\frac{b}{4}\)

Đặt \(\frac{a}{3}=\frac{b}{4}=k\)\(\Rightarrow a=3k,b=4k\)

\(\Rightarrow D=\frac{a^3+3^3}{b^3+4^3}=\frac{\left(3k\right)^3+3^3}{\left(4k\right)^3+4^3}\)

\(=\frac{3^3\left(k^3+1\right)}{4^3\left(k^3+1\right)}=\frac{3^3}{4^3}=\frac{27}{64}\)

TL: 
8 nhé 

HNJK

\(P=\dfrac{3x^2+1-3x^2+6x-3}{3x^2+1}=1-\dfrac{3\left(x-1\right)^2}{3x^2+1}\le1\)

\(P_{max}=1\) khi \(x=1\)

w

360:4/9=160

160 : 2/5 = 64  vay 360-160-64 =136

\(\left(3x-1\right).\left(\frac{-1}{2}x+5\right)=0.\)

\(TH1:3x-1=0\)

\(3x=0+1\)

\(3x=1\)

\(x=\frac{1}{3}\)

\(TH2:\frac{-1}{2}x+5=0\)

\(\frac{-1}{2}x=-5\)

\(x=-5\div\frac{-1}{2}\)

\(x=10\)

\(\left(3x-1\right).\left(\frac{-1}{2}x+5\right)=0.\)

TH1: 

\(3x-1=0\)

\(3x=0+1\)

\(3x=1\)

\(x=1\div3\)

\(x=\frac{1}{3}\)

TH2: 

\(\frac{-1}{2}x+5=0\)

\(\frac{-1}{2}x=0-5\)

\(\frac{-1}{2}x=-5\)

\(x=-5\div\frac{-1}{2}\)

\(\Leftrightarrow x=-5.\left(-2\right)\)

\(x=10\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{3}\\x=10\end{cases}}\)

Câu hỏi của đề bài là j?

Ok bạn

a) \(\frac{-1}{2}+\frac{5}{6}+\frac{1}{3}=\frac{1}{3}+\frac{1}{3}=\frac{2}{3}.\)

b) \(\frac{-3}{8}+\frac{7}{4}+\frac{1}{12}=\frac{3}{8}+\frac{1}{12}=\frac{36}{96}+\frac{8}{96}=\frac{48}{96}=\frac{1}{2}\)

c)  \(\frac{3}{5}\div\left(\frac{1}{4}\div\frac{7}{5}\right)=\frac{3}{5}\div\frac{5}{28}=\frac{3}{5}.\frac{28}{5}=\frac{84}{25}\)

d) \(\frac{10}{11}+\frac{4}{11}\div4-\frac{-1}{8}=\left(\frac{14}{11}\div4\right)-\frac{-1}{8}=\frac{7}{22}-\frac{1}{8}=\frac{56}{176}-\frac{22}{176}=\frac{34}{176}=\frac{17}{88}\)

e) \(\frac{5}{13}.\frac{8}{15}+\frac{5}{13}.\frac{26}{15}-\frac{5}{13}.\frac{8}{15}=\frac{5}{13}.\left(\frac{8}{15}+\frac{26}{15}-\frac{8}{15}\right)=\frac{5}{13}.\frac{26}{15}=\frac{130}{195}=\frac{26}{39}\)

\(\frac{5}{6}+\frac{7}{13}+\frac{17}{9}+\frac{19}{13}+\frac{1}{9}+\frac{7}{6}\)

\(=\left(\frac{5}{6}+\frac{7}{6}\right)+\left(\frac{17}{9}+\frac{1}{9}\right)+\left(\frac{19}{13}+\frac{7}{13}\right)\)

\(=\frac{12}{6}+\frac{18}{9}+\frac{26}{13}\)

\(=2+2+2\)

\(=4+2\)

\(=6\)

\(\frac{5}{6}+\frac{7}{13}+\frac{17}{9}+\frac{19}{13}+\frac{1}{9}+\frac{7}{6}.\)

\(=\left(\frac{5}{6}+\frac{7}{6}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)+\left(\frac{17}{9}+\frac{1}{9}\right)\)

\(=\frac{12}{6}+\frac{26}{13}+\frac{18}{9}\)

\(=2+2+2\)

\(=6\)

Tổng số lít nước là  : \(24\times120=2880\text{ lít}\)

Nếu mỗi thùng chứa được 160 lít nước thì số thùng cần để chứa nước là : 

\(2880:160=18\text{ thùng}\)