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a: =>\(\dfrac{5x-15+4x-8}{\left(x-2\right)\left(x-3\right)}=\dfrac{1}{x}\)
=>\(\dfrac{9x-23}{\left(x-2\right)\left(x-3\right)}=\dfrac{1}{x}\)
=>9x^2-23x=x^2-5x+6
=>8x^2-18x-6=0
=>\(x=\dfrac{9\pm\sqrt{129}}{8}\)
b: =>\(\dfrac{12x+1}{11x-4}=\dfrac{20x+17-20x+8}{18}=\dfrac{25}{18}\)
=>216x+18=275x-100
=>-59x=-118
=>x=2
ĐKXĐ x\(\ne\) \(\dfrac{4}{11}\)
\(\Rightarrow\left(12x+1\right)18+\left(10x-4\right)\left(11x-4\right)2=\left(20x+17\right)\left(11x-4\right)\)
\(\Leftrightarrow216x+18+\left(110x^2-40x-44x+16\right)2=220x^2-80x+187x-68\)
\(\Leftrightarrow216x+18+220x^2-168x+32=220x^2+107x-68\Leftrightarrow220x^2-48x+50=220x^2+107x-68\Leftrightarrow220x^2+107x+48x-220x^2=50+68\Leftrightarrow155x=138\Leftrightarrow x=\dfrac{138}{155}\left(TM\right)\)Vậy...
f: =>\(\dfrac{14}{3\left(x-4\right)}-\dfrac{x+2}{x-4}=\dfrac{-3}{2\left(x-4\right)}-\dfrac{5}{6}\)
=>28-6(x+2)=-9-5(x-4)
=>28-6x-12=-9-5x+20
=>-6x+16=-5x+11
=>-x=-5
=>x=5
d: =>\(\dfrac{12x+1}{11x-4}=\dfrac{20x+17-20x+8}{18}=\dfrac{25}{18}\)
=>25(11x-4)=18(12x+1)
=>275x-100=216x+18
=>59x=118
=>x=2
f: =>\(\dfrac{14}{3\left(x-4\right)}-\dfrac{x+2}{x-4}=\dfrac{-3}{2\left(x-4\right)}-\dfrac{5}{6}\)
=>28-6(x+2)=-9-5(x-4)
=>28-6x-12=-9-5x+20
=>-6x+16=-5x+11
=>-x=-5
=>x=5
bạn tách một câu vài câu hỏi chứ đừng gộp như thế này ko ai trả lời đâu
a: =>\(4x-5=2x-2+x=3x-2\)
=>x=3
b: \(\Leftrightarrow7x-35=3x+6\)
=>4x=41
=>x=41/4
c: =>(2x+5)(x+5)-2x^2=0
=>2x^2+10x+5x+25-2x^2=0
=>15x=-25
=>x=-5/3
e: \(\Leftrightarrow\dfrac{11}{x}=\dfrac{9x-36+2x+2}{\left(x+1\right)\left(x-4\right)}\)
=>11(x^2-3x-4)=x(11x-34)
=>11x^2-33x-44=11x^2-34x
=>x=44
\(a,\frac{7}{x+2}=\frac{3}{x-5}\)
\(\Rightarrow7\left(x-5\right)=3\left(x+2\right)\)
\(\Rightarrow7x-35=3x+6\)
\(\Rightarrow7x-3x=6+35\)
\(\Rightarrow4x=41\)
\(\Rightarrow x=\frac{41}{4}\)
\(b,\frac{2x+5}{2x}-\frac{x}{x+5}=0\)
\(\Rightarrow\frac{2x+5}{2x}=\frac{x}{x+5}\)
\(\Rightarrow\left(2x+5\right)\left(x+5\right)=2x\cdot x\)
\(\Rightarrow2x^2+10x+5x+25=2x^2\)
\(\Rightarrow2x^2+15x+25-2x^2=0\)
\(\Rightarrow15x+25=0\)
\(\Rightarrow15x=-25\)
\(\Rightarrow x=\frac{-5}{3}\)
\(c,\frac{12x+1}{11x-4}+\frac{10x-4}{9}=\frac{20x+17}{18}\)
\(\Rightarrow\frac{12x+1}{11x-4}=\frac{20x+17}{18}-\frac{10x-4}{9}\)
\(\Rightarrow\frac{12x+1}{11x-4}=\frac{25}{18}\)
\(\Rightarrow\left(12x+1\right)\cdot18=25\cdot\left(11x-4\right)\)
\(\Rightarrow216x+18=275x-100\)
\(\Rightarrow216x-275x=-100-18\)
\(\Rightarrow-59x=-118\)
\(\Rightarrow x=2\)
\(\frac{12x+1}{11x-4}+\frac{10x-4}{9}=\frac{20x+17}{18}\left(ĐKXĐ:x\ne\frac{4}{11}\right).\)
\(\Leftrightarrow\frac{18.\left(12x+1\right)}{18.\left(11x-4\right)}+\frac{2.\left(11x-4\right).\left(10x-4\right)}{18.\left(11x-4\right)}=\frac{\left(11x-4\right).\left(20x+17\right)}{18.\left(11x-4\right)}\)
\(\Rightarrow18.\left(12x+1\right)+2.\left(11x-4\right).\left(10x-4\right)=\left(11x-4\right).\left(20x+17\right)\)
\(\Leftrightarrow216x+18+\left(22x-8\right).\left(10x-4\right)=220x^2+187x-80x-68\)
\(\Leftrightarrow216x+18+220x^2-88x-80x+32=220x^2+107x-68\)
\(\Leftrightarrow48x+50+220x^2=220x^2+107x-68\)
\(\Leftrightarrow48x+50+220x^2-220x^2-107x+68=0\)
\(\Leftrightarrow118-59x=0\)
\(\Leftrightarrow59x=118-0\)
\(\Leftrightarrow59x=118\)
\(\Leftrightarrow x=118:59\)
\(\Leftrightarrow x=2\left(TM\right).\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{2\right\}.\)
Chúc bạn học tốt!