\(a^2-6b^2=-ab\Rightarrow\frac{a^2-6b^2}{ab}=-1\)

\(\Leftrightarrow\frac{a}{b}-\frac{6b}{a}=-1\)

dat m=\(\frac{a}{b}\)

\(\Leftrightarrow m-\frac{6}{m}=-1\Rightarrow m^2-6=m\)

\(\Leftrightarrow\left\{\begin{matrix}m=2\\m=-3\end{matrix}\right.\)

vi m=\(\frac{a}{b}\)

nen \(\left\{\begin{matrix}\frac{a}{b}=2\\\frac{a}{b}=-3\end{matrix}\right.\Leftrightarrow\left\{\begin{matrix}a=2b\\a=-3b\left(loai\right)\end{matrix}\right.\)

thay a=2b vao M ta duoc ket qua la\(\frac{4}{5}\)

Từ \(a^2-6b^2=-ab\Rightarrow a^2-6b^2+ab=0\)

\(\Rightarrow a^2+3ab-2ab-6b^2=0\)

\(\Rightarrow a\left(a+3b\right)-2b\left(a+3b\right)=0\)

\(\Rightarrow\left(a+3b\right)\left(a-2b\right)=0\)

\(\Rightarrow\left[\begin{matrix}a+3b=0\\a-2b=0\end{matrix}\right.\)\(\Rightarrow\left[\begin{matrix}a=-3b\\a=2b\end{matrix}\right.\)

*)Xét \(a=-3b\) thay vào M ta có:

\(M=\frac{2\cdot3\left(-b\right)\cdot b}{2\left(-3b\right)^2-3b^2}=\frac{-6b^2}{15b^2}=-\frac{2}{5}\)

*)Xét \(a=2b\) thay vào M ta có:

\(M=\frac{2\cdot2b\cdot b}{2\cdot\left(2b\right)^2-3b^2}=\frac{4b^2}{8b^2-3b^2}=\frac{4b^2}{5b^2}=\frac{4}{5}\)

Bài 1:

a^2-5ab-6b^2=0

=>a^2-6ab+ab-6b^2=0

=>a*(a-6b)+b(a-6b)=0

=>(a-6b)(a+b)=0

=>a=-b hoặc a=6b

TH1: a=-b

\(A=\dfrac{-2b-b}{-3b-b}+\dfrac{5b+b}{-3b+b}=\dfrac{-3}{-4}+\dfrac{6}{-2}=\dfrac{3}{4}-3=-\dfrac{9}{4}\)

TH2: a=6b

\(A=\dfrac{12b-b}{18b-b}+\dfrac{5b-6b}{18b+b}=\dfrac{11}{17}+\dfrac{-1}{19}=\dfrac{192}{323}\)

Từ \(a^2-6b^2=-ab\Rightarrow a^2-6b^2+ab=0\)

\(\Rightarrow a^2+3ab-2ab-6b^2=0\)

\(\Rightarrow a\left(a+3b\right)-2b\left(a+3b\right)=0\)

\(\Rightarrow\left(a+3b\right)\left(a-2b\right)=0\)

\(\Rightarrow\orbr{\begin{cases}a+3b=0\\a-2b=0\end{cases}}\Rightarrow\orbr{\begin{cases}a=-3b\\a=2b\end{cases}}\)

\(M=\frac{2\cdot3\left(-b\right)\cdot b}{2\left(-3b\right)^2-3b^2}=\frac{-6b^2}{15b^2}=-\frac{2}{5}\)

\(M=\frac{2\cdot2b\cdot b}{2\cdot\left(2b\right)^2-3b^2}=\frac{4b^2}{8b^2-3b^2}=\frac{4b^2}{5b^2}=\frac{4}{5}\)

Giải

a, 2A+3B=0 <=> \(\dfrac{10}{2m+1}+\dfrac{12}{2m-1}=0\)

<=>10(2m-1)+ 12(2m+1) =0

<=> 44m +2 =0 

<=> m=-1/22

b, AB= A+B <=> \(\dfrac{20}{\left(2m-1\right)\left(2m+1\right)}=\dfrac{5}{2m+1}+\dfrac{4}{2m-1}\)

<=> 20 = 5(2m -1) + 4(2m+1) 

<=> 20 = 18m - 1

<=> m=7/6

a^2+9ab-22b^2=0

=>a^2+11ab-2ab-2b^2=0

=>(a+11b)(a-2b)=0

=>a=2b hoặc a=-11b

TH1: a=2b

\(M=\dfrac{2b+3b}{4b-b}=\dfrac{5}{3}\)

TH2: a=-11b

\(M=\dfrac{-11b+3b}{-22b-b}=\dfrac{8}{23}\)