4 phần x+3 bằng 2phần x-1
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a,Ta có \(\frac{x}{6}=\frac{2}{3}\)
\(\Rightarrow3x=12\Rightarrow x=4\)
Vậy x = 4
b, \(\left(\frac{4}{7}+\frac{8}{9}\right)-\frac{5}{9}=\frac{4}{7}+\frac{8}{9}-\frac{5}{9}\)
\(=\frac{4}{7}+\left(\frac{8}{9}-\frac{5}{9}\right)\)
\(=\frac{4}{7}+\frac{1}{3}\)
\(=\frac{19}{21}\)
Bài 1 mình nhầm. x phần 6 = 4 phần 7 mới đúng. Cảm ơn bạn nhé
\(\dfrac{x+2}{x-2}-\dfrac{x-2}{x+2}=\dfrac{10}{-x^2+4}\)
\(\Leftrightarrow\left(x+2\right)^2-\left(x-2\right)^2=-10\)
\(\Leftrightarrow x^2+4x+4-x^2+4x-4=-10\)
=>8x=-10
hay x=-5/4
vậy hông
\(\frac{2^2}{2^{x+y}}=8\)và \(\frac{3^2.\left(x+y\right)}{3^{5y}}=343\)
\(\left(\dfrac{3}{4}+\dfrac{2}{3}\right):\dfrac{17}{4}-\dfrac{3}{4}\)
\(=\left(\dfrac{9}{12}+\dfrac{8}{12}\right):\dfrac{17}{4}-\dfrac{3}{4}\)
\(=\dfrac{17}{12}:\dfrac{17}{4}-\dfrac{3}{4}\)
\(=\dfrac{17.4}{17.12}-\dfrac{3}{4}\)
\(=\dfrac{1}{3}-\dfrac{3}{4}\)
\(=\dfrac{4}{12}-\dfrac{9}{12}\)
\(=-\dfrac{5}{12}\)
a) Ta có: \(\left(2x+3\right)^2-4\left(x-2\right)\left(x+2\right)\)
\(=4x^2+12x+9-4\left(x^2-4\right)\)
\(=4x^2+12x+9-4x^2+16\)
\(=12x+25\)
b) Ta có: \(\dfrac{x+6}{x^2-4}-\dfrac{2}{x\left(x+2\right)}\)
\(=\dfrac{x\left(x+6\right)}{x\left(x+2\right)\left(x-2\right)}-\dfrac{2\left(x-2\right)}{x\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{x^2+6x-2x+4}{x\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{x^2+4x+4}{x\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{\left(x+2\right)^2}{x\left(x+2\right)\left(x-2\right)}\)
\(=\dfrac{x+2}{x\left(x-2\right)}\)
\(C=\dfrac{7}{10}\cdot\dfrac{8}{3}\cdot20\cdot\dfrac{3}{8}\cdot\dfrac{5}{28}\)
\(=7\cdot2\cdot\dfrac{5}{28}=\dfrac{5}{2}\)
\(D=\left(-6.17+3+\dfrac{5}{9}-2-\dfrac{36}{97}\right)\cdot\left(\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12}\right)=0\)
\(\dfrac{4}{x+3}=\dfrac{2}{x-1}\left(x\ne-3;x\ne1\right)\)
suy ra: \(4\left(x-1\right)=2\left(x+3\right)\\ < =>4x-4=2x+6\\ < =>4x-2x=6+4\\ < =>2x=10\\ < =>x=5\left(tm\right)\)
\(\dfrac{4}{x+3}=\dfrac{2}{x-1}\text{ĐKXĐ}:x\ne-3;1\)
\(\Leftrightarrow\dfrac{4\left(x-1\right)}{\left(x+3\right)\left(x-1\right)}=\dfrac{2\left(x+3\right)}{\left(x+3\right)\left(x-1\right)}MTC:\left(x+3\right)\left(x-1\right)\)
\(\Rightarrow4x-4=2x+6\)
\(\Leftrightarrow4x-4-2x-6=0\)
\(\Leftrightarrow2x-10=0\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\left(\text{nhận}\right)\)
\(\text{Vậy phương trình có tập nghiệm là }S=\left\{5\right\}\)