Giải các phương trình sau:
a) \(x+\frac{2x+\frac{x-1}{5}}{3}=1-\frac{3x-\frac{1-2x}{3}}{5}\)
b) \(\frac{3x-1-\frac{x-1}{2}}{3}-\frac{2x+\frac{1-2x}{3}}{2}=\frac{\frac{3x-1}{2}}{5}\)
Bài 2: Giải phương trình:
a) \(x+\frac{2x+\frac{x-1}{5}}{3}=1-\frac{3x-\frac{1-2x}{3}}{5}\)
b) \(\frac{3x-1-\frac{x-1}{2}}{3}-\frac{2x+\frac{1-2x}{3}}{2}=\frac{\frac{3x-1}{2}-6}{5}\)
Giải các phương trình sau
a, \(\frac{x+5}{3}-\frac{x-3}{5}=\frac{5}{x-3}-\frac{3}{x+5}\)
b,\(\frac{3x-1}{x-1}-\frac{2x+5}{x+3}+\frac{4}{x^2+2x+3}\)
c,\(\frac{2x}{3x^2-x+2}-\frac{7x}{3x^2+5x+2}=1\)
Các bạn giúp mk nha
\(\Leftrightarrow\frac{5\left(x+5\right)-3\left(x-3\right)}{15}=\frac{5\left(x+5\right)-3\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}\)
\(\Leftrightarrow\frac{2x+34}{15}=\frac{2x+34}{x^2+2x-15}\Leftrightarrow\orbr{\begin{cases}2x+34=0\\x^2+2x-15=15\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-17\\x^2+2x-30=0\end{cases}}\)
Từ đó tìm được \(S=\left\{-17;\sqrt{31}-1;-\sqrt{31}-1\right\}\)
Giải các phương trình sau:
a) \(x+\frac{2x+\frac{x-1}{5}}{3}=1-\frac{3x-\frac{1-2x}{3}}{5}\)
b) \(\frac{3x-1-\frac{x-1}{2}}{3}-\frac{2x+\frac{1-2x}{3}}{2}=\frac{\frac{3x-1}{2}}{5}\)
c) \(\frac{x-23}{24}+\frac{x-23}{25}=\frac{x-23}{26}+\frac{x-23}{27}\)
Giải phương trình
\(\frac{x+5}{3x-6}-\frac{1}{2}=\frac{2x-3}{2x-4}\)\(\frac{x+5}{3x-6}-\frac{1}{2}=\frac{2x-3}{2x-4}\)
Giải các phương trình.
a) \(\frac{2.\left(1-3x\right)}{5}-\frac{2+3x}{10}=7-\frac{3.\left(2x+1\right)}{4}\)b) \(\frac{3x+2}{2}-\frac{3x+1}{6}=2x+\frac{5}{3}\)
c) 3x-5=7
d) \(\frac{5}{x+3}=\frac{3}{x-1}\)
e) -2x+14=0
f) 2x.(x-3)+5.(x-3)=0
g) (x2-4)-(x-2).(3-2x)=0
h) 2x3+6x2=x2+3x
1) Giải các phương trình:
a) \(\frac{x-3}{5}-\frac{2x-1}{10}=\frac{x+1}{2}+\frac{1}{4}\)
b)\(\frac{x+3}{2}-\frac{2-1}{3}-1=\frac{x+5}{6}\)
c)\(\frac{x-1}{4}-\frac{5-2x}{9}=3x-\frac{2}{3}\)
d)\(\frac{2x-1}{4}+\frac{x-3}{3}=\frac{4x-2}{3}-\frac{6x+7}{12}\)
e)\(\frac{3x-2}{5}+\frac{x-1}{9}=\frac{14x-3}{15}-\frac{2x+1}{9}\)
\(\frac{x-3}{5}-\frac{2x-1}{10}=\frac{x+1}{2}+\frac{1}{4}\)
\(< =>\frac{\left(x-3\right).4}{20}-\frac{\left(2x-1\right).2}{20}=\frac{\left(x+1\right).10}{20}+\frac{5}{20}\)
\(< =>4x-12-4x+2=10x+10+5\)
\(< =>10x=-10-10-5=-25\)
\(< =>x=-\frac{25}{10}=-\frac{5}{2}\)
\(\frac{x+3}{2}-\frac{2x-1}{3}-1=\frac{x+5}{5}\)
\(< =>\frac{\left(x+3\right).15}{30}-\frac{\left(2x-1\right).10}{30}-\frac{30}{30}=\frac{\left(x+5\right).5}{30}\)\(< =>15x+45-20x+10-30=5x+25\)
\(< =>-5x+25=5x+25< =>10x=0< =>x=0\)
\(\frac{x-1}{4}-\frac{5-2x}{9}=3x-\frac{2}{3}\)
\(< =>\frac{\left(x-1\right).9}{36}-\frac{\left(5-2x\right).4}{36}=\frac{3x.36}{36}-\frac{2.12}{36}\)
\(< =>\left(x-1\right).9-\left(5-2x\right).4=108x-24\)
\(< =>9x-9-20+8x=108x-24\)
\(< =>108x-17x=-29+24\)
\(< =>91x=-5< =>x=-\frac{5}{91}\)
Giải phương trình sau: \(\frac{3x-1-\frac{x-1}{2}}{3}-\frac{2x+\frac{1-2x}{3}}{2}=\frac{\frac{3x-1}{2}}{5}\)
\(\frac{3x-1-\frac{x-1}{2}}{3}-\frac{2x+\frac{1-2x}{3}}{2}=\frac{\frac{3x-1}{2}}{5}\)
\(\frac{6.\left(3x-1\right)-3x-1}{3}-\frac{12x+2\left(1-2x\right)}{2}=\frac{3\left(3x-1\right)}{5}\)
\(\Leftrightarrow\)\(\frac{18x-6-3x+3}{3}-\frac{12x+2-4x}{2}=\frac{9x-3}{5}\)
\(\Leftrightarrow\)\(\frac{15x-3}{3}-\frac{8x+2}{2}=\frac{9x-3}{5}\)
\(\Leftrightarrow\)\(10\left(15x-3\right)-15\left(8x+2\right)=6\left(9x-3\right)\)
\(\Leftrightarrow\)\(150x-30-120x-30=54x-18\)
\(\Leftrightarrow\)\(150x-120x-54x=-18+30+30\)
\(\Leftrightarrow-24x=42\)
\(\Leftrightarrow x=-\frac{7}{4}\)
Giải phương trình sau: \(\frac{3x-1-\frac{x-1}{2}}{3}-\frac{2x+\frac{1-2x}{3}}{2}=\frac{\frac{3x-1}{2}}{5}\)
<=>\(\frac{6x-2-x+1}{6}-\frac{6x+1-2x}{6}=\frac{3x-1}{10}\)
<=>\(\frac{5\left(x-2\right)}{30}=\frac{3\left(3x-1\right)}{30}\)
<=> 5x - 2 = 9x - 3
<=> 4x = 1
=> x = 1/4
Vậy S = {1/4}
Bài 1: Giải các phương trình sau:
a) \(\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)
b) \(\frac{7x-1}{6}+2x=\frac{16-x}{5}\)
Bài 2: Giải các phương trình sau:
a) \(x+\frac{2x+\frac{x-1}{5}}{3}=1-\frac{3x-\frac{1-2x}{3}}{5}\)
b) \(\frac{3x-1-\frac{x-1}{2}}{3}-\frac{2x+\frac{1-2x}{3}}{2}=\frac{\frac{3x-1}{2}-6}{5}\)
\(1a,\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow\frac{3\left(2x+1\right)^2}{15}-\frac{5\left(x-1\right)^2}{15}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow\frac{12x^2+12x+3}{15}-\frac{5x^2-10x+5}{15}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow12x^2+12x+3-5x^2+10x-5=7x^2-14x-5\)
\(\Leftrightarrow36x=-3\)
\(x=-\frac{1}{12}\)
Vậy ................
\(b,\frac{7x-1}{6}+2x=\frac{16-x}{5}\)
\(\Leftrightarrow\frac{5\left(7x-1\right)}{30}+\frac{30.2x}{30}=\frac{6\left(16-x\right)}{30}\)
\(\Leftrightarrow35x-5+60x=96-6x\)
\(\Leftrightarrow101x=101\)
\(\Leftrightarrow x=1\)
Vậy ....................
Bài 1:
c) \(\frac{\left(x-2\right)^2}{3}-\frac{\left(2x-3\right).\left(2x+3\right)}{8}+\frac{\left(x-4\right)^2}{6}=0\)
\(\Leftrightarrow\frac{8.\left(x-2\right)^2}{8.3}-\frac{3.\left(2x-3\right).\left(2x+3\right)}{3.8}+\frac{4.\left(x-4\right)^2}{4.6}=0\)
\(\Leftrightarrow\frac{8.\left(x^2-4x+4\right)}{24}-\frac{3.\left(4x^2-9\right)}{24}+\frac{4.\left(x^2-8x+16\right)}{24}=0\)
\(\Rightarrow8.\left(x^2-4x+4\right)-3.\left(4x^2-9\right)+4.\left(x^2-8x+16\right)=0\)
\(\Leftrightarrow8x^2-32x+32-\left(12x^2-27\right)+4x^2-32x+64=0\)
\(\Leftrightarrow8x^2-32x+32-12x^2+27+4x^2-32x+64=0\)
\(\Leftrightarrow123-64x=0\)
\(\Leftrightarrow64x=123-0\)
\(\Leftrightarrow64x=123\)
\(\Leftrightarrow x=123:64\)
\(\Leftrightarrow x=\frac{123}{64}.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{\frac{123}{64}\right\}.\)
Chúc bạn học tốt!
Bài 1:
a) \(\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow\frac{3\left(4x^2+4x+1\right)}{15}-\frac{5\left(x^2-2x+1\right)}{15}=\frac{7x^2-14x-5}{15}\)
\(\Leftrightarrow12x^2+12x+3-5x^2+10x-5-7x^2+14x+5=0\)
\(\Leftrightarrow36x+3=0\)
\(\Leftrightarrow x=12\)
Vậy phương trình có nghiệm là x = 12