a) \(\frac{x+3}{x-2}-\frac{2x+3}{x+2}=\frac{2x^2+5x+12}{x^2-4}\)

ĐKXĐ: \(\left\{\begin{matrix}x\ne2\\x\ne-2\end{matrix}\right.\)

\(\Rightarrow\left(x+3\right)\left(x+2\right)-\left(2x+3\right)\left(x-2\right)=2x^2+5x+12\)

\(\Leftrightarrow x^2+2x+3x+6-2x^2+4x-3x+6-2x^2-5x-12=0\)

\(\Leftrightarrow-3x^2+4x=0\)

\(\Leftrightarrow3x^2-4x=0\)

\(\Leftrightarrow x\left(3x-4\right)=0\)

\(\Leftrightarrow\left[\begin{matrix}x=0\\3x-4=0\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=0\\3x=4\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=0\left(tmđk\right)\\x=\frac{4}{3}\left(tmđk\right)\end{matrix}\right.\)

Vậy: \(x=0;\frac{4}{3}\)

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b) Ta có: \(\frac{2x+5}{x-3}+\frac{x-1}{x+3}=\frac{x^2+6x+18}{x^2-9}\)

ĐKXĐ: \(\left\{\begin{matrix}x\ne3\\x\ne-3\end{matrix}\right.\)

\(\Leftrightarrow\frac{\left(2x+5\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{\left(x-1\right)\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}=\frac{x^2+6x+18}{\left(x+3\right)\left(x-3\right)}\)

\(\Rightarrow\left(2x+5\right)\left(x+3\right)+\left(x-1\right)\left(x-3\right)=x^2+6x-18\)

\(\Leftrightarrow2x^2+6x+5x+15+x^2-3x-x+3-x^2-6x-18=0\)

\(\Leftrightarrow2x^2+x=0\)

\(\Leftrightarrow x\left(2x+1\right)=0\)

\(\Leftrightarrow\left[\begin{matrix}x=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=0\\2x=-1\end{matrix}\right.\Leftrightarrow\left[\begin{matrix}x=0\\x=-\frac{1}{2}\end{matrix}\right.\)

Vậy: \(x=0;-\frac{1}{2}\)

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a) x+3/x-2 - 2x+3/x+2 =2x²+5x+12/x²-4

đkxđ : x khác -2; x khác 2

<=>(x+3).(x+2)/(x-2).(x+2) - (2x+3).(x-2)/(x-2).(x+2) = 2x²+5x+12/(x-2).(x+2)

=>x²+2x+3x+6 - 2x²-4x+3x-6 =2x²+5x+12

<=>x²-2x²-2x² + 2x+3x-4x-5x = 12-6+6

<=>-3x² - 4x = 0

<=>-x(3x-4)=0

<=>-x=0

<=>3x-4=0

<=>-x=0

<=>3x=4

<=>-x/-1=0/-1

<=>3x/3=4/3

<=>x=0(tm)

<=>x=4/3(tm)

vậy phương trình có nghiệm x=0 ; x=4/3.

d: =>4x+6=15x-12

=>4x-15x=-12-6=-18

=>-11x=-18

hay x=18/11

e: =>\(45x+27=12+24x\)

=>21x=-15

hay x=-5/7

f: =>35x-5=96-6x

=>41x=101

hay x=101/41

g: =>3(x-3)=90-5(1-2x)

=>3x-9=90-5+10x

=>3x-9=10x+85

=>-7x=94

hay x=-94/7

\(\Leftrightarrow\frac{\frac{x-3+5}{5}}{4}=\frac{\frac{4x-3}{6}}{6}\Leftrightarrow\frac{x+2}{20}=\frac{4x-3}{36}\Leftrightarrow36x+72=80x-60\Leftrightarrow44x=132\Rightarrow x=2\)

\(\Leftrightarrow\frac{\frac{10x+x+2}{2}}{9}-\frac{\frac{x+3+75}{5}}{12}=x-2\)\(\Leftrightarrow\frac{11x+2}{18}-\frac{x+78}{60}=x-2\)\(\Leftrightarrow\left(\frac{11}{18}-\frac{1}{60}-1\right)x+\left(\frac{2}{18}-\frac{78}{60}+2\right)=0\).Giải típ nha, ko có Casio nên mk ko bấm

\(\Leftrightarrow5x+\frac{x+2}{18}-x-\frac{x+3+75}{60}+2=0\Leftrightarrow\left(5+\frac{1}{18}-1-\frac{1}{60}\right)x+\left(\frac{2}{18}-\frac{78}{60}+2\right)=0\).Giải típ nha

1/ Đặt \(\sqrt{9-x^2}=a\ge0\)

\(\Rightarrow\frac{9-a^2}{3+a}+\frac{1}{12-4a}=1\)

\(\Leftrightarrow4a^2-20a+25=0\)

\(\Leftrightarrow a=\frac{5}{2}\)

\(\Rightarrow\sqrt{9-x^2}=\frac{5}{2}\)

\(\Leftrightarrow x^2=\frac{11}{4}\)

\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{\sqrt{11}}{2}\\x=\frac{\sqrt{11}}{2}\end{cases}}\)

2/ \(\frac{9}{x^2}+\frac{2x}{\sqrt{2x^2+9}}-1=0\)

\(\Leftrightarrow\frac{9+2x^2}{x^2}+\frac{2x}{\sqrt{2x^2+9}}-3=0\)

Đặt \(\frac{x}{\sqrt{2x^2+9}}=a\)

\(\Rightarrow\frac{1}{a^2}+2a-3=0\)

\(\Leftrightarrow2a^3-3a^2+1=0\)

\(\Leftrightarrow\left(a-1\right)^2\left(2a+1\right)=0\)

Làm nốt nhé

3/ \(x+\frac{x}{\sqrt{x^2-1}}=2\sqrt{2}\)

\(\Leftrightarrow x-\sqrt{2}+\frac{x-\sqrt{2x^2-2}}{\sqrt{x^2-1}}=0\)

\(\Leftrightarrow x-\sqrt{2}+\frac{2-x^2}{\sqrt{x^2-1}.\left(x+\sqrt{2x^2-2}\right)}=0\)

\(\Leftrightarrow\left(x-\sqrt{2}\right)\left(1+\frac{\sqrt{2}+x}{\sqrt{x^2-1}.\left(x+\sqrt{2x^2-2}\right)}\right)=0\)

\(\Leftrightarrow x=\sqrt{2}\)

\(\frac{x-3}{5}-\frac{2x-1}{10}=\frac{x+1}{2}+\frac{1}{4}\)

\(< =>\frac{\left(x-3\right).4}{20}-\frac{\left(2x-1\right).2}{20}=\frac{\left(x+1\right).10}{20}+\frac{5}{20}\)

\(< =>4x-12-4x+2=10x+10+5\)

\(< =>10x=-10-10-5=-25\)

\(< =>x=-\frac{25}{10}=-\frac{5}{2}\)

\(\frac{x+3}{2}-\frac{2x-1}{3}-1=\frac{x+5}{5}\)

\(< =>\frac{\left(x+3\right).15}{30}-\frac{\left(2x-1\right).10}{30}-\frac{30}{30}=\frac{\left(x+5\right).5}{30}\)\(< =>15x+45-20x+10-30=5x+25\)

\(< =>-5x+25=5x+25< =>10x=0< =>x=0\)

\(\frac{x-1}{4}-\frac{5-2x}{9}=3x-\frac{2}{3}\)

\(< =>\frac{\left(x-1\right).9}{36}-\frac{\left(5-2x\right).4}{36}=\frac{3x.36}{36}-\frac{2.12}{36}\)

\(< =>\left(x-1\right).9-\left(5-2x\right).4=108x-24\)

\(< =>9x-9-20+8x=108x-24\)

\(< =>108x-17x=-29+24\)

\(< =>91x=-5< =>x=-\frac{5}{91}\)

a)\(\frac{\frac{x-3}{5}+1}{4}=\frac{\frac{2x}{3}-\frac{1}{2}}{6}\)

\(\Rightarrow\frac{\frac{x-3+5}{5}}{4}=\frac{\frac{4x}{6}-\frac{3}{6}}{6}\)

\(\Rightarrow\frac{\frac{x+2}{5}}{4}=\frac{\frac{4x-3}{6}}{6}\)

\(\Rightarrow\frac{x+2}{5}:4=\frac{4x-3}{6}:6\)

\(\Rightarrow\frac{x+2}{5}.\frac{1}{4}=\frac{4x-3}{6}.\frac{1}{6}\)

\(\Rightarrow\frac{x+2}{20}=\frac{4x-3}{36}\)

\(\Rightarrow36.\left(x+2\right)=20.\left(4x-3\right)\)

\(\Rightarrow36x+72=80x-60\)

\(\Rightarrow72+60=80x-36x\)

\(\Rightarrow132=44x\)

\(\Rightarrow x=\frac{132}{44}=3\)

Vậy x=3

b)Bn làm tương tự phần a nha

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