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1.
\(\frac{2x+3}{4}-\frac{5x+3}{6}=\frac{3-4x}{12}\)
\(MC:12\)
Quy đồng :
\(\Rightarrow\frac{3.\left(2x+3\right)}{12}-\left(\frac{2.\left(5x+3\right)}{12}\right)=\frac{3x-4}{12}\)
\(\frac{6x+9}{12}-\left(\frac{10x+6}{12}\right)=\frac{3x-4}{12}\)
\(\Leftrightarrow6x+9-\left(10x+6\right)=3x-4\)
\(\Leftrightarrow6x+9-3x=-4-9+16\)
\(\Leftrightarrow-7x=3\)
\(\Leftrightarrow x=\frac{-3}{7}\)
2.\(\frac{3.\left(2x+1\right)}{4}-1=\frac{15x-1}{10}\)
\(MC:20\)
Quy đồng :
\(\frac{15.\left(2x+1\right)}{20}-\frac{20}{20}=\frac{2.\left(15x-1\right)}{20}\)
\(\Leftrightarrow15\left(2x+1\right)-20=2\left(15x-1\right)\)
\(\Leftrightarrow30x+15-20=15x-2\)
\(\Leftrightarrow15x=3\)
\(\Leftrightarrow x=\frac{3}{15}=\frac{1}{5}\)
a) \(\frac{x+\frac{x+1}{5}}{3}=1-\frac{2x-\frac{1-2x}{34}}{5}\)
\(\Leftrightarrow\frac{\frac{5x+x+1}{5}}{3}=1-\frac{\frac{68x-1+2x}{34}}{5}\)
\(\Leftrightarrow\frac{6x+1}{15}=1-\frac{70-1}{170}\)
\(\Leftrightarrow\frac{6x+1}{15}+\frac{70x-1}{170}-1=0\)
\(\Leftrightarrow\frac{34\left(6x+1\right)+3\left(70x-1\right)-510}{510}=0\)
\(\Leftrightarrow204x+34+210x-3-510=0\)
\(\Leftrightarrow414x-479=0\)
\(\Leftrightarrow x=\frac{479}{414}\)
Vậy tập nghiệm của phương trình là \(S=\left\{\frac{479}{414}\right\}\)
<=> \(\frac{3\left(2x+1\right)^2}{15}-\frac{5\left(x-1\right)^2}{15}-\frac{7x^2-14x-5}{15}=0\)
<=> \(\frac{12x^2+12x+3}{15}-\frac{5x^2-10x+5}{15}-\frac{7x^2-14x-5}{15}=0\)
<=> \(\frac{12x^2+12x+3-5x^2+10x-5-7x^2+14x+5}{15}=0\)
=> 36x + 3 = 0
<=> 36x = -3
<=> x = -1/12
Vậy S = { -1/12 }
\(\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow\frac{4x^2+4x+1}{5}-\frac{x^2-2x+1}{3}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow\frac{12x^2+12x+3}{15}-\frac{5x^2-10x+5}{15}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow12x^2+12x+3-5x^2+10x-5-7x^2+14x+5=0\)
\(\Leftrightarrow36x+3=0\Leftrightarrow x=-\frac{3}{36}=-\frac{1}{12}\)
\(\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow3\left(2x+1\right)^2-5\left(x-1\right)^2=7x^2-14x-5\)
\(\Leftrightarrow3\left(4x^2+4x+1\right)-5\left(x^2-2x+1\right)=7x^2-14x-5\)
\(\Leftrightarrow12x^2+12x+3-5x^2+10x-5=7x^2-14x-5\)
\(\Leftrightarrow36x=-3\)
\(\Leftrightarrow x=-\frac{1}{12}\)
\(\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow\frac{3\left(4x^2+4x+1\right)}{15}-\frac{5\left(x^2-2x+1\right)}{15}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow12x^2+12x+3-5x^2+10x-5=7x^2-14x-5\)
\(\Leftrightarrow\)12x2+12x+3-5x2+10x-5-7x2+14x+5=0
\(\Leftrightarrow\)36x+3=0
\(\Leftrightarrow\)36x=-3
\(\Leftrightarrow\)x=\(-\frac{1}{12}\)
Vậy pt có tập nghiêm S={\(-\frac{1}{12}\)}
\(\frac{25x-655}{95}-\frac{5\left(x-12\right)}{209}=\frac{89-3x-\frac{2\left(x-18\right)}{5}}{11}\)
\(< =>\frac{5x-131}{19}=\frac{1631-52x-\frac{38x-684}{5}}{209}\)
\(< =>\left(5x-131\right)209=\left(1631-52x-\frac{38x-684}{5}\right)19\)
\(< =>55x-1441=1631-52x-\frac{38x-684}{5}\)
\(< =>3072-107x=\frac{38x-684}{5}\)
\(< =>\left(3072-107x\right)5=38x-684\)
\(< =>15360-535x-38x-684=0\)
\(< =>14676=573x< =>x=\frac{14676}{573}=\frac{4892}{191}\)
nghệm xấu thế
\(\frac{8\left(x+22\right)}{45}-\frac{7x+149+\frac{6\left(x+12\right)}{5}}{9}=\frac{x+35+\frac{2\left(x+50\right)}{9}}{5}\)
\(< =>\frac{8x+176}{45}-\frac{41x+817}{45}=\frac{11x+415}{45}\)
\(< =>993-33x-11x-415=0\)
\(< =>578=44x< =>x=\frac{289}{22}\)
phương trình tương đương
<=>\(\frac{3\left(2x+1\right)^2}{15}-\frac{5\left(x-1\right)^2}{15}=\frac{7x^2-14x-5}{15}\)
<=>\(\frac{3\left(4x^2+4x+1\right)}{15}-\frac{5\left(x^2-2x+1\right)}{15}=\frac{7x^2-14x-5}{15}\)
<=>\(\frac{12x^2+12x+3-5x^2+10x-5}{15}=\frac{7x^2-14x-5}{15}\)
<=>\(\frac{7x^2+22x-2}{15}=\frac{7x^2-14x-5}{15}\)<=>7\(x^2+22x-2=7x^2-14x-5\)
<=>22x+14x=-5+2
<=>36x=-3
<=>>x=\(\frac{-3}{36}=\frac{-1}{12}\)