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Bài làm
a) \(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x-4}\)
\(\Leftrightarrow\frac{3x+2}{3x-2}-\frac{6}{3x+2}=\frac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\)
\(\Leftrightarrow\frac{(3x+2)\left(3x+2\right)}{(3x-2)\left(3x+2\right)}-\frac{6\left(3x-2\right)}{(3x+2)\left(3x-2\right)}=\frac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\)
\(\Rightarrow\left(3x+2\right)^2-\left(18x-12\right)=9x^2\)
\(\Leftrightarrow9x^2+12x+4-18x+12x-9x^2=0\)
\(\Leftrightarrow6x+4=0\)
\(\Leftrightarrow x=-\frac{4}{6}\)
\(\Leftrightarrow x=-\frac{2}{3}\)
Vậy x = -2/3 là nghiệm.
@Tao Ngu :))@ 9x-4 không tách thành (3x+4)(3x-4) được đâu bạn. Chỗ đó phải là: 9x2-4
Bài thiếu đkxđ của x \(\hept{\begin{cases}3x-2\ne0\\2+3x\ne0\end{cases}\Leftrightarrow\hept{\begin{cases}3x\ne2\\3x\ne-2\end{cases}\Leftrightarrow}\hept{\begin{cases}x\ne\frac{2}{3}\\x\ne\frac{-2}{3}\end{cases}\Leftrightarrow}x\ne\pm\frac{2}{3}}\)
Ta có \(\frac{7x-5}{8}=\frac{3x+1}{5}\)
<=> \(35x-25=24x+8\)
<=> \(35x-24x=8+25\)
<=> \(11x=33\)
<=> x=3
Vậy phương trình có ngiệm duy nhất x=3
\(\frac{7x-5}{8}=\frac{3x+1}{5}\) MTC= 40
\(5\left(7x-5\right)=8\left(3x+1\right)\)
\(35x-25=24x+8\)
\(35x-24x=8+25\)
\(11x=33\)
\(\Rightarrow x=3\)
a) 7x - 35 = 0
<=> 7x = 0 + 35
<=> 7x = 35
<=> x = 5
b) 4x - x - 18 = 0
<=> 3x - 18 = 0
<=> 3x = 0 + 18
<=> 3x = 18
<=> x = 5
c) x - 6 = 8 - x
<=> x - 6 + x = 8
<=> 2x - 6 = 8
<=> 2x = 8 + 6
<=> 2x = 14
<=> x = 7
d) 48 - 5x = 39 - 2x
<=> 48 - 5x + 2x = 39
<=> 48 - 3x = 39
<=> -3x = 39 - 48
<=> -3x = -9
<=> x = 3
1. \(\frac{3x-7}{5}=\frac{2x-1}{3}\)
<=> 3(3x-7)=5(2x-1)
<=> 9x-21=10x-5
<=> -21+5=10x-9x
<=> x=-16
2. \(\frac{3x-7}{2}+\frac{2x-1}{3}=-16\)
<=> \(\frac{3\left(3x-7\right)}{6}+\frac{2\left(2x-1\right)}{6}=\frac{-96}{6}\)
=> 9x-21+4x-2=-96
<=> 13x-23=-96
<=> 13x=-73
<=> x=\(\frac{-73}{13}\)
3. \(x-\frac{x+1}{3}=\frac{2x+1}{5}\)
<=> \(\frac{15x}{15}-\frac{5\left(x+1\right)}{15}=\frac{3\left(2x+1\right)}{15}\)
=> 15x-5x-5=6x+3
<=> 15x-5x-6x=3+5
<=> 4x=8
<=> x=2
4. \(\frac{7-3x}{12}+\frac{3}{4}=2\left(x-2\right)+\frac{5-\left(5-2x\right)}{6}\)
<=>\(\frac{7-3x}{12}+\frac{9}{12}=\frac{24\left(x-2\right)}{12}+\frac{2\left[5-\left(5-2x\right)\right]}{12}\)
=> 7-3x+9=24x-48+4x
<=> -3x-24x-4x=-48-7
<=> -31x=-55
<=> x= \(\frac{55}{31}\)
5. \(\frac{2x-1}{3}-\frac{5x+2}{7}=x+13\)
<=> \(\frac{7\left(2x-1\right)}{21}-\frac{3\left(5x+2\right)}{21}=\frac{21\left(x+13\right)}{21}\)
=> 14x-7-15x-6=21x+273
<=> 14x-15x-21x=273+7+6
<=> -22x=286
<=> x= -13
a/\(\Leftrightarrow3\left(3x-7\right)=5\left(2x-1\right)\Leftrightarrow9x-21=10x-5\Leftrightarrow x=-16\)
b/\(\Leftrightarrow\frac{9x-21+4x-2}{6}=-16\)\(\Leftrightarrow13x-23=-96\Leftrightarrow x=x=-\frac{73}{13}\)
c/\(\Leftrightarrow\frac{3x-x+1}{3}-\frac{2x+1}{5}=0\Leftrightarrow\left(2x+1\right)\left(\frac{1}{3}-\frac{1}{5}\right)=0\Leftrightarrow x=-\frac{1}{2}\)
\(\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}\)
\(\Leftrightarrow\left(\frac{x-1}{13}-1\right)-\left(\frac{2x-13}{15}-1\right)=\left(\frac{3x-15}{27}-1\right)-\left(\frac{4x-27}{29}-1\right)\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}=\frac{3\left(x-14\right)}{27}-\frac{4\left(x-14\right)}{29}\)
\(\Leftrightarrow\left(x-14\right)\left(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\right)=0\)
<=> x-14=0
<=> x=14
\(\frac{x-1}{13}-\frac{2x-13}{15}=\frac{3x-15}{27}-\frac{4x-27}{29}\)
\(\Leftrightarrow\frac{x-1}{13}-1-\frac{2x-13}{15}+1=\frac{3x-15}{27}-1-\frac{4x-27}{29}+1\)
\(\Leftrightarrow\left(\frac{x-1}{13}-1\right)-\left(\frac{2x-13}{15}-1\right)=\left(\frac{3x-15}{27}-1\right)-\left(\frac{4x-27}{29}-1\right)\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2x-28}{15}=\frac{3x-42}{27}-\frac{4x-56}{29}\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}=\frac{3\left(x-14\right)}{27}-\frac{4\left(x-14\right)}{29}\)
\(\Leftrightarrow\frac{x-14}{13}-\frac{2\left(x-14\right)}{15}-\frac{3\left(x-14\right)}{27}+\frac{4\left(x-14\right)}{29}=0\)
\(\Leftrightarrow\left(x-14\right)\left(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\right)=0\)
Vì \(\frac{1}{13}-\frac{2}{15}-\frac{3}{27}+\frac{4}{29}\ne0\)
\(\Rightarrow x-14=0\)\(\Leftrightarrow x=14\)
Vậy tập nghiệm của phương trình là \(S=\left\{14\right\}\)
Cộng từng hạng tử của hai vế với 1 , ta suy ra được tử chung là 3x+21=0
=> x=-7