1, Tìm x
a, 4x - (7+ 5x) = 15 + (-29)
b,\(\frac{x}{11}=\frac{x+4}{33}\)
2. Rút gọn
a, \(\frac{3.7.11}{33\cdot9}\)
b,\(\frac{5^3.2^4}{4.10^2.11}\)
c.\(\frac{8.5-8.2}{32}\)
a)\(\frac{1}{6}x+\frac{1}{10}-\frac{4}{15}x+1=\)\(0\)
b)\(\left(\frac{1}{7}x-\frac{2}{7}\right).\left(-\frac{1}{5}x+\frac{3}{5}\right).\left(\frac{1}{3}x+\frac{4}{3}\right)=0\)
c)\(\frac{1}{2}x-\frac{11}{15}:\frac{33}{35}=-\frac{1}{3}\)
Tìm x biết:
a, \(\frac{1}{6}x+\frac{1}{10}-\frac{4}{15}x+1=0\)
\(\Leftrightarrow-\frac{1}{10}x=-\frac{11}{10}\)
\(\Leftrightarrow x=11\)
b,\(\left(\frac{1}{7}x-\frac{2}{7}\right)\left(-\frac{1}{5}x+\frac{3}{5}\right)\left(\frac{1}{3}x+\frac{4}{3}\right)=0\)
\(\Leftrightarrow\frac{1}{7}x-\frac{2}{7}=0\)hoặc \(-\frac{1}{5}x+\frac{3}{5}=0\)hoặc \(\frac{1}{3}x+\frac{4}{3}=0\)
+) \(\frac{1}{7}x-\frac{2}{7}=0\Leftrightarrow\frac{1}{7}x=\frac{2}{7}\Leftrightarrow x=2\)
+)\(-\frac{1}{5}x+\frac{3}{5}=0\Leftrightarrow-\frac{1}{5}x=-\frac{3}{5}\Leftrightarrow x=3\)
+)\(\frac{1}{3}x+\frac{4}{3}=0\Leftrightarrow\frac{1}{3}x=-\frac{4}{3}\Leftrightarrow x=-4\)
c, \(\frac{1}{2}x-\frac{11}{15}:\frac{33}{35}=-\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{2}x-\frac{7}{9}=-\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{2}x=\frac{4}{9}\)
\(\Leftrightarrow x=\frac{8}{9}\)
a/ \(\frac{1}{6}x+\frac{1}{10}-\frac{4}{15}x+1=0\)
\(\Rightarrow-\frac{1}{10}x=-\frac{11}{10}\)
\(\Rightarrow x=11\)
b/ \(\left(\frac{1}{7}x-\frac{2}{7}\right)\left(-\frac{1}{5}x+\frac{3}{5}\right)\left(\frac{1}{3}x+\frac{4}{3}\right)=0\)
\(\Rightarrow\frac{1}{7}x-\frac{2}{7}=0\Rightarrow\frac{1}{7}x=\frac{2}{7}\Rightarrow x=2\)
hoặc \(-\frac{1}{5}x+\frac{3}{5}=0\Rightarrow-\frac{1}{5}x=-\frac{3}{5}\Rightarrow x=3\)
hoặc \(\frac{1}{3}x+\frac{4}{3}=0\Rightarrow\frac{1}{3}x=-\frac{4}{3}\Rightarrow x=-4\)
Vậy x = 2, x = 3, x = -4
c/ \(\frac{1}{2}x-\frac{11}{15}:\frac{33}{35}=-\frac{1}{3}\)
\(\Rightarrow\frac{1}{2}x-\frac{7}{9}=-\frac{1}{3}\)
\(\Rightarrow\frac{1}{2}x=\frac{4}{9}\Rightarrow x=\frac{8}{9}\)
Vậy x = 8/9
Bài 4 Giải các bất phương trình sau :
31 , \(\frac{-3x^2-x+4}{x^2+3x+5}>0\)
32 , \(\frac{4x^2+3x-1}{x^2+5x+7}>0\)
33 , \(\frac{5x^2+3x-8}{x^2-7x+6}< 0\)
34 , \(\frac{2x-5}{x^2-6x-7}< \frac{1}{x-3}\)
35 , \(\frac{x^2-5x+6}{x^2+5x+6}\ge\frac{x+1}{x}\)
Tìm x:\(a,\frac{6x-5}{-7}=\frac{5x-3}{-5}\\ b,\frac{12-7x}{-13}=\frac{4-3x}{-5}\\ c,\frac{2x+4}{7}=\frac{4x-2}{15}\)
a) \(\frac{6x-5}{-7}=\frac{5x-3}{-5}\)
=> -5(6x - 5) = -7(5x - 3)
=> -30x + 25 = -35x + 21
=> -30x + 25 + 35x - 21 = 0
=> (-30x + 35x) + (25 - 21) = 0
=> 5x + 4 = 0
=> 5x = -4
=> x = -4/5
b) \(\frac{12-7x}{-13}=\frac{4-3x}{-5}\)
=> -5(12 - 7x) = -13(4 - 3x)
=> -60 + 35x = -52 + 39x
=> -60 + 35x + 52 - 39x = 0
=> (-60 + 52) + (35x - 39x) = 0
=> -8 - 4x = 0
=> -8 = 4x
=> x = -2
c) \(\frac{2x+4}{7}=\frac{4x-2}{15}\)
=> 15(2x + 4) = 7(4x - 2)
=> 30x + 60 = 28x - 14
=> 30x + 60 - 28x + 14 = 0
=> 2x + 74 = 0
=> 2x = -74
=> x = -37
A=\(\frac{\left(X+2\right)^2}{X}\left(1-\frac{X^2}{X+2}\right)\)và B=\(\frac{4}{x^2-4x+4}\)
a) rút gọnA
b) tìm x thuộc Z để A nguyên dương
c) tính C=\(\frac{A}{B}\)
d) tìm giá trị của x để C>0
a, \(A=\frac{\left(x+2\right)^2}{x}\left(1-\frac{x^2}{x+2}\right)=\frac{\left(x+2\right)^2}{x}\left(\frac{x+2-x^2}{x+2}\right)\)
\(=\frac{-\left(x+2\right)^2\left(x-2\right)\left(x+1\right)}{x\left(x+2\right)}=\frac{-\left(x\pm2\right)\left(x+1\right)}{x}\)
c, Theo bài ra ta có : \(C=\frac{A}{B}\)hay \(\frac{\frac{-\left(x\pm2\right)\left(x+1\right)}{x}}{\frac{4}{\left(x-2\right)^2}}=\frac{\frac{-\left(x+2\right)\left(x+1\right)}{x}}{\frac{4}{x-2}}\)
d, Theo bài ra ta có :
\(C>0\)hay \(\frac{\frac{-\left(x+2\right)\left(x+1\right)}{x}}{\frac{4}{x-2}}>0\)
\(\Leftrightarrow\frac{-\left(x+2\right)\left(x+1\right)}{x}.\frac{x-2}{4}>0\)
\(\Leftrightarrow-\left(x+2\right)\left(x+1\right)>0\Leftrightarrow\left(x+2\right)\left(x+1\right)>0\)
\(\Leftrightarrow x>-2;x>-1\Rightarrow x>-1\)
a,Tính nhanh:
A=1,(11)+2,(22)+3,(33)+...+8,(88)
b,Cho:\(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\) CMR:\(\frac{4x-3y}{2016}=\frac{5y-4z}{2017}\frac{3z-5x}{2018}\)
A)\(\left(x-11\right)+\frac{3x}{x-11}=3+\frac{33}{x-11}\)
B)\(\frac{7-2x}{x-1}=\frac{1-4x}{x+2}\)
C)\(\frac{3-2x}{x+1}=2+\frac{1-4x}{x-2}\)
D)\(\frac{109x-4}{111x+1}-1=0\)
E)\(\frac{x^2-7}{x}=x-\frac{1}{2}\)
F)\(\frac{x+1}{x+2}=3\)
a) \(\left(x-11\right)+\frac{3x}{x-11}=3+\frac{33}{x-11}\)
\(\Leftrightarrow x+\frac{3x}{x-11}-\frac{33}{x-11}=14\)
\(\Leftrightarrow x^2-11x+3x-33=14x-154\)
\(\Leftrightarrow x^2-22x+121=0\)
\(\Leftrightarrow\left(x-11\right)^2=0\Leftrightarrow x=11\)
Vậy .......
b) \(\frac{7-2x}{x-1}=\frac{1-4x}{x+2}\Leftrightarrow\left(7-2x\right)\left(x+2\right)=\left(1-4x\right)\left(x-1\right)\)
\(\Leftrightarrow7x-2x^2+14-4x=x-4x^2-1+4x\)
\(\Leftrightarrow2x^2=-15\)(vô lí)
Vậy pt vô nghiệm
c) \(\frac{3-2x}{x+1}=2+\frac{1-4x}{x-2}\)
\(\Leftrightarrow\left(3-2x\right)\left(x-2\right)=2\left(x+1\right)\left(x-2\right)+\left(1-4x\right)\left(x+1\right)\)
\(\Leftrightarrow3x-2x^2-6x+4x=2x^2+2x-4x-4+x-4x^2+1-4x\)
\(\Leftrightarrow6x=-3\Leftrightarrow x=-\frac{1}{2}\)
Vậy.........
(gửi trước 3 câu)
d) \(\frac{109x-4}{111x+1}-1=0\Leftrightarrow109x-4=111x+1\Leftrightarrow2x=-5\Leftrightarrow x=-\frac{5}{2}\)
Vậy x=-5/2
e) \(\frac{x^2-7}{x}=x-\frac{1}{2}\Leftrightarrow\frac{x^2-7}{x}-\frac{x^2}{x}=-\frac{1}{2}\Leftrightarrow-\frac{7}{x}=\frac{1}{2}\Leftrightarrow x=-14\)
f) \(\frac{x+1}{x+2}=3\Leftrightarrow x+1=3x+6\Leftrightarrow2x=7\Leftrightarrow x=\frac{7}{2}\)
d) \(\frac{109x-4}{111x+1}=1\)
\(\Rightarrow\frac{109x-4}{111x+1}=1\)
\(\Rightarrow109x-4=111x+1\)
\(\Rightarrow-2x=5\)
\(\Rightarrow x=-2,5\)
Vậy x = -2,5
e) \(\frac{x^2-7}{x}=x-\frac{1}{2}\)
\(\Rightarrow\frac{x^2-7}{x}=\frac{2x-1}{2}\)
\(\Rightarrow\left(x^2-7\right)2=x\left(2x-1\right)\)
\(\Rightarrow2x^2-14=2x^2-x\)
\(\Rightarrow x=14\)
Vậy x = 14
f) \(\frac{x+1}{x+2}=3\)
\(\Rightarrow x+1=3\left(x+2\right)\)
\(\Rightarrow x+1=3x+6\)
\(\Rightarrow2x=-5\)
\(\Rightarrow x=-2,5\)
Vậy x = -2,5
tìm phần nguyên
\(A=\left(\frac{-5}{11}\right).\frac{7}{15}+\frac{11}{-5}.\frac{30}{33}\)
\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{x.\left(x+1\right)}\)(x∈Z)
\(C=\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)
\(D=\frac{1}{3}-\left[\left(-\frac{5}{4}\right)-\left(\frac{1}{4}+\frac{3}{8}\right)\right]\)
giúp mk nhé, mk tk, mk thanks nhiều
\(A=\left(-\frac{5}{11}\right).\frac{7}{15}+\frac{11}{-5}.\frac{30}{33}\)
\(A=-\frac{7}{33}+-2\)
\(A=-\frac{73}{33}\)
[ A] = -2
\(D=\frac{1}{3}-\left[\left(-\frac{5}{4}\right)-\left(\frac{1}{4}+\frac{3}{8}\right)\right]\)
\(D=\frac{1}{3}-\left[\left(-\frac{5}{4}\right)-\frac{5}{8}\right]\)
\(D=\frac{1}{3}-\left(-\frac{15}{8}\right)\)
\(D=\frac{53}{24}\)
\(\left[D\right]=2\)
Thu gọn:
a) 2x(x2-2)-3(4-3x)-2x3+5x
b)\(\frac{x^2+1}{x^2-3x}+\frac{3}{x}-\frac{x}{x-3}\)
c)\(\frac{5}{2x-3}+\frac{2}{2x+3}-\frac{2x-33}{9-4x^2}\)
Tìm x, biết:
a) \(\frac{x+1}{35}+\frac{x+3}{33}=\frac{x+5}{31}+\frac{x+7}{29}\)
b) \(\frac{x-10}{1994}+\frac{x-8}{1996}+\frac{x-6}{1998}+\frac{x-4}{2000}+\frac{x-2}{2002}=\frac{x-2002}{2}+\frac{x-2000}{4}+\frac{x-1998}{6}+\frac{x-1996}{8}+\frac{x-1994}{10}\)
a/ (X+1)/35+1+(x+3)/33+1 =(x+5)/31+(x+7)/29+1+1
=>(x+36)/35+(x+36)/33-(x+36)/31-(x+36)/27=0
=>(X+36)(1/35+1/33-1/31-1/29)=0
=> x+36=0(vì c=vế 2 luôn luôn khác 0)
=>x=-36
b/ CMTT câu a
trừ tung phân số cho 1 ta được x=2004