1.Tìm các số thực a, b, c biết:
\(\frac{5x^2-2}{x^3-3x-2}=\frac{a}{x-2}+\frac{b}{x+1}+\frac{c}{\left(x+1\right)^2}\)
2.giải các phương trình sau:
a) \(\frac{x+3}{35}+\frac{x+3}{45}+\frac{x+3}{54}=0\)
b)\(\frac{2x-1}{85}+\frac{2x-1}{58}=\frac{2x-1}{62}\)
c)\(\frac{x=1}{100}+\frac{x+2}{99}+\frac{x+3}{98}=-3\)
d)\(\frac{x+13}{2010}+\frac{x+12}{2011}=\frac{x+11}{2012}+\frac{x+10}{2013}\)
e)\(\frac{845-x}{345}+\frac{771-x}{271}=\frac{687-x}{187}+\frac{529-x}{29}\)
ĐẠI SỐ
1. Giải các phương trình sau :
a) \(\frac{25x-655}{95}-\frac{5\left(x-12\right)}{209}=\frac{89-3x-\frac{2\left(x-18\right)}{5}}{11}\)
b) \(\frac{8\left(x+22\right)}{45}-\frac{7x+149+\frac{6\left(x+12\right)}{5}}{9}=\frac{x+35+\frac{2\left(x+50\right)}{9}}{5}\)
c) \(\frac{x+\frac{2\left(3-x\right)}{5}}{14}-\frac{5x-4\left(x-1\right)}{24}=\frac{7x+2+\frac{9-3x}{5}}{12}+\frac{2}{3}\)
2. Giải các bất phương trình sau :
a) \(5+\frac{x+4}{5}< x-\frac{x-2}{2}+\frac{x+3}{3}\)
b) \(x+1-\frac{x-1}{3}< \frac{2x+3}{2}+\frac{x}{3}+5\)
c) \(\frac{\left(3x-2\right)^2}{3}-\frac{\left(2x+1\right)^2}{3}\le x\left(x+1\right)\)
d) \(\frac{2x+3}{4}-\frac{x+1}{3}\ge\frac{1}{2}-\frac{3-x}{5}\)
1) giải phương trình:
a) \(\left(2x+3\right)\left(\frac{3x+8}{2-7x}+1\right)=\left(x+5\right)\left(\frac{3x+8}{2-7x}+1\right)\)
b) \(\frac{7x+10}{x+1}\left(x^2-x-2\right)-\frac{7x+10}{x+1}\left(2x^2-3x-5\right)=0\)
c) \(\frac{2x+5}{x+3}+1=\frac{4}{x^2+2x-3}-\frac{3x-1}{1-x}\)
d) \(\frac{13}{2x^2+x-21}+\frac{1}{2x+7}+\frac{6}{9-x^2}=0\)
e) \(\frac{x-49}{50}+\frac{x-50}{49}=\frac{49}{x-50}+\frac{50}{x-49}\)
f) \(\frac{1+\frac{x}{x+3}}{1-\frac{x}{x+3}}=3\)
Giải các phương trình sau :
a. 3x - 2 (5 + 2x) = 45 - 2x
b. \(\frac{x-3}{5}=6-\frac{1-2x}{3}\)
c.\(\frac{5\left(x-1\right)+2}{6}-\frac{7x-1}{4}=\frac{2\left(2x+1\right)}{7}-5\)
d. (x - 1) (5x + 3) = (3x - 8) (x - 1)
e. (x - 1) (x2 + 5x - 2) - (x3 - 1) = 0
f.\(\frac{x-17}{33}+\frac{x-21}{29}+\frac{x}{25}=4\)
g. \(\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+1}{61}+\frac{x+7}{59}\)
h.\(\frac{x+5}{2015}+\frac{x+4}{2014}+\frac{x+4}{1002}+\frac{x+6}{1003}=6\)
k.\(\frac{148-x}{25}+\frac{169-x}{23}+\frac{186-x}{21}+\frac{199-x}{19}=10\)
Giải các phương trình sau :
a. 3x - 2 (5 + 2x) = 45 - 2x
b. \(\frac{x-3}{5}=6-\frac{1-2x}{3}\)
c.\(\frac{5\left(x-1\right)+2}{6}-\frac{7x-1}{4}=\frac{2\left(2x+1\right)}{7}-5\)
d. (x - 1) (5x + 3) = (3x - 8) (x - 1)
e. (x - 1) (x2 + 5x - 2) - (x3 - 1) = 0
f.\(\frac{x-17}{33}+\frac{x-21}{29}+\frac{x}{25}=4\)
g. \(\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+1}{61}+\frac{x+7}{59}\)
h.\(\frac{x+5}{2015}+\frac{x+4}{2014}+\frac{x+4}{1002}+\frac{x+6}{1003}=6\)
k.\(\frac{148-x}{25}+\frac{169-x}{23}+\frac{186-x}{21}+\frac{199-x}{19}=10\)
Giải các phương trình:
a) \(\frac{1}{x-1}-\frac{3x^2}{x^3-1}=\frac{2x}{x^2+x+1}\)
b) \(\frac{3}{\left(x-1\right)\left(x-2\right)}+\frac{2}{\left(x-3\right)\left(x-1\right)}=\frac{1}{\left(x-2\right)\left(x-3\right)}\)
c) \(1+\frac{1}{x+2}=\frac{12}{8+x^3}\)
d) \(\frac{13}{\left(x-3\right)\left(2x+7\right)}+\frac{1}{2x+7}=\frac{6}{\left(x-3\right)\left(x+3\right)}\)
giải bất phương trình
a.\(\frac{2x-3}{35}+\frac{x\left(x-2\right)}{7}>\frac{x^2}{7}-\frac{2x-3}{5}\)
b.\(\frac{6x+1}{18}+\frac{x+3}{12}\le\frac{5x+3}{6}+\frac{12-5x}{9}\)
2.Giải phương trình
b.\(\frac{\left|2x-1\right|}{x-1}+1=\frac{1}{x-1}\)
Giải pt:
\(a.\frac{x}{3}-\frac{5x}{6}-\frac{15x}{12}=\frac{x}{4}-5\)
\(b.\frac{8x-3}{4}-\frac{3x-2}{2}=\frac{2x-1}{2}+\frac{x+3}{4}\)
\(c.\frac{x-1}{2}-\frac{x+1}{15}-\frac{2x-13}{6}=0\)
\(d.\frac{3\left(3-x\right)}{8}+\frac{2\left(5-x\right)}{3}=\frac{1-x}{2}-2\)
Giải các phương trình sau :
\(a,6x^2-5x+3=2x-3x\left(3-2x\right)\)
\(b,\frac{2\left(x-4\right)}{4}-\frac{3+2x}{10}=x+\frac{1-x}{5}\)
\(c,\frac{2x}{3}+\frac{3x-5}{4}=\frac{3\left(2x-1\right)}{2}-\frac{7}{6}\)
\(d,\frac{6x+5}{2}-\frac{10x+3}{4}=2x+\frac{2x+1}{2}\)
\(e,\left(x-4\right)\left(x+4\right)-2\left(3x-2\right)=\left(x-4\right)^2\)
Giải các phương trình sau:
a) \(\frac{x+5}{x^2-5x}-\frac{x+25}{2x^2-50}=\frac{x-5}{2x^2+10x}\).
b) \(\frac{1}{3-x}-\frac{1}{x+1}=\frac{x}{x-3}-\frac{\left(x-1\right)^2}{x^2-2x-3}\).
c) \(\frac{x+1}{x^2+x+1}-\frac{x-1}{x^2-x+1}=\frac{2\left(x+2\right)^2}{x^6-1}\).
d) \(\frac{x}{x-3}-\frac{x}{x-5}=\frac{x}{x-4}-\frac{x}{x-6}\).
