a: ĐKXĐ: x<>-3
b: \(Q=\left(\dfrac{x}{x^2-3x+9}-\dfrac{11}{\left(x+3\right)\left(x^2-3x+9\right)}+\dfrac{1}{x+3}\right)\cdot\dfrac{x+3}{x^2-1}\)
\(=\dfrac{x^2+3x-11+x^2-3x+9}{\left(x+3\right)\left(x^2-3x+9\right)}\cdot\dfrac{x+3}{x^2-1}\)
\(=\dfrac{2x^2-2}{x^2-1}\cdot\dfrac{1}{x^2-3x+9}=\dfrac{2}{x^2-3x+9}\)
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)\(\frac{x+1}{x+2}=3\)
1) tính
a) \(\frac{4}{x+2}+\frac{3}{2-x}+\frac{12}{x^2-4}\)
b) \(x+\frac{x-1}{2}+\frac{x-2}{3}\)
c) \(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{3x-6}{4-9x^2}\)
d) x - 2 - \(\frac{x^2-10}{x+2}\)
e) \(\frac{1}{2x-2y}-\frac{1}{2x+2y}+\frac{y}{y^2-x^2}\)
f) \(\frac{1}{a+1}-\frac{3}{a^3+1}+\frac{3}{a^2-a+1}\)
g) \(\frac{4-2x+x^2}{x+2}-2-x\)
h)\(\frac{1}{x^3-x}-\frac{1}{x^2-x}+\frac{2}{x^2-1}\)
j) \(\frac{1}{2x+3}-\frac{1}{2x-3}+\frac{x-2}{2x^2-x-3}\)
a) GTNN: A=x(x-3)(x-4)(x-7)
b) GTNN: B=2x\(^2\)+y\(^2\)-2xy-2x+3
c) GTNN: A=\(\frac{2}{6x-5-9x^2}\)
d) GTNN: B=\(\frac{3x^2+9x+\text{1}7}{3x^2+9x+7}\)
e) GTNN: A=\(\frac{3-4x}{x^2+\text{1}}\)
f) GTLN: A=\(\frac{3-4x}{x^2+\text{1}}\)
Rút gọn biểu thức:
a, \(\frac{x^4+15x+7}{2x^3+2}.\frac{x}{14x^2+1}.\frac{4x^3+4}{x^4+15x+7}\)
b, \(\frac{x^7+3x^2+2}{x^3-1}.\frac{3x}{x+1}.\frac{x^2+x+1}{x^7+3x^2+2}\)
tim dieu kien cua x de a co nghia va rut gon a
Xác định a,b,c để :
a, \(\frac{6x^2-x-1}{x^3-x}=\frac{a}{x}+\frac{b}{x-1}+\frac{c}{x+1}\)
b, \(\frac{6x^3-5x^2+3}{x^4-1}=\frac{a}{x-1}+\frac{b}{x+1}+\frac{cx+d}{x^2+1}\)
Cho M=\(\left(\frac{4}{x-4}-\frac{4}{x+4}\right).\left(\frac{x^2+8x+16}{32}\right)\)
a) Tìm x để giá trị của biểu thức bằng 0
b) Tính M biết \(x=\frac{-3}{8}\)
c) Tìm \(x\in Z\) để \(M\in Z\)
d) tìm GTLN của K biết \(K=\frac{M.3}{x^2+4x+24}\)
1 . Giải phương trình :
a) \(7x-5=13-5x\) d)\(\frac{2x-3}{3}-\frac{x-3}{6}=\frac{4x+3}{5}-17\)
b) \(13-7x=4x-20\) e) \(\frac{x+1}{58}+\frac{x+2}{57}=\frac{x+3}{56}+\frac{x+4}{55}\)
c) \(\frac{2x-1}{3}-\frac{5x+2}{7}=x+13\)
2 . Cho hai phương trình ẩn x :
\(3x+3=0\) ( 1 )
\(5-kx=7\) ( 2 )
Tìm giá trị của k sao cho nghiệm của phương trình ( 1 ) là nghiệm của phương trình ( 2 ) .
A)\(\frac{x+1}{4}-\frac{x+2}{5}+\frac{x+4}{7}-\frac{x+5}{8}+\frac{x+7}{10}-\frac{x+9}{12}=0\)
B)\(\frac{x}{2004}+\frac{x+1}{2005}+\frac{x+2}{2006}+\frac{x+3}{2006}=4\)
C)\(\frac{x+2}{x-3}+\frac{x-2}{x+3}-\frac{2\left(x^2+6\right)}{x^2-9}=0\)
D)\(\frac{x^2-15x+1}{x+17}=x-2\)
E)\(\frac{x}{x^2+5x+6}=\frac{2}{x^2+3x+1}\)
