1. Tính:
a) \(\frac{18}{\left(x-3\right)\left(x^2-9\right)}-\frac{3}{x^2-6x+9}-\frac{x}{x^2-9}\)
b) \(\frac{x}{5x+5}-\frac{x}{10x-10}\)
c) \(\frac{x+9}{x^2-9}-\frac{3}{x^2+3x}\)
\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\\ \left(\frac{3x}{1-3n}+\frac{2n}{3x+1}\right):\left(\frac{6x^2+10x}{1-6x+9x^2}\right)\\ \left(\frac{9}{x^3-9n}+\frac{1}{x+3}\right):\left(\frac{x}{3n+9}\right)\)
\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)
= \(\frac{3x\left(x-y\right)}{5.2.\left(x+y\right)\left(x-y\right)}-\frac{x\left(x+y\right)}{10\left(x^2-y^2\right)}\)
= \(\frac{3x^2-3xy-x^2-xy}{10\left(x^2-y^2\right)}\)
= \(\frac{3x\left(x-y\right)}{10\left(x^2-y^2\right)}\)
= \(\frac{3x}{10\left(x+y\right)}\)
Trừ phân thức
a) \(\frac{1}{3x-2}-\frac{1}{3x+2}-\frac{3x-6}{4-9x^2}\)
b) \(\frac{18}{\left(x-3\right)\left(x^2-9\right)}-\frac{3}{x^2-6x+9}-\frac{x^2}{x^2-9}\)
\(\frac{1}{3x-2}-\frac{1}{3x+2}-\frac{3x-6}{4-9x^2}\)
\(=\frac{3x+2}{9x^2-4}-\frac{3x-2}{9x^2-4}+\frac{3x-6}{9x^2-4}\)
\(=\frac{3x+2-3x+2+3x-6}{9x^2-4}\)
\(=\frac{3x-2}{9x^2-4}\)
\(=\frac{1}{3x+2}\)
\(\frac{18}{\left(x-3\right)\left(x^2-9\right)}-\frac{3}{x^2-6x+9}-\frac{x^2}{x^2-9}\)
\(=\frac{18}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\) \(-\frac{3\left(x+3\right)}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\)\(-\frac{x^2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x-3\right)}\)
\(=\frac{18-3x-9-x^3+3x^2}{\left(x-3\right)^2\left(x+3\right)}\)
\(=\frac{-x^3+3x^2-3x+9}{\left(x-3^2\right)\left(x+3\right)}\)
\(=\frac{\left(-x^2-3\right)\left(x-3\right)}{\left(x-3^2\right)\left(x+3\right)}\)
\(=\frac{-x^2-3}{\left(x-3\right)\left(x+3\right)}\)
học tốt
Rút gọn
a) \(\left(\frac{4}{x^3-9x}+\frac{1}{x+3}\right):\left(\frac{x-3}{x^2+3x}-\frac{x}{3x+9}\right)\)
b) \(\left(\frac{2}{x-2}-\frac{2}{x+2}\right).\frac{x^2+4x+4}{8}\)
c) \(\left(\frac{3x}{1-3x}+\frac{2x}{3x+1}\right):\frac{6x^2+10x}{1-6x+9x^2}\)
thực hiện phép trừ phân thức không cùng mẫu:
a/\(\frac{8+9}{x^2-9}-\frac{3}{x^2+3x}\) b/ \(\frac{18}{\left(x-3\right)\left(x^2-9\right)}-\frac{3}{x^2-6x+9}-\frac{x}{x^2-9}\)
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) \(\frac{2x+3}{4}-\frac{x+1}{3}\ge\frac{1}{2}-\frac{3-x}{5}\)
\(\frac{25x-655}{95}-\frac{5\left(x-12\right)}{209}=\frac{89-3x-\frac{2\left(x-18\right)}{5}}{11}\)
\(< =>\frac{5x-131}{19}=\frac{1631-52x-\frac{38x-684}{5}}{209}\)
\(< =>\left(5x-131\right)209=\left(1631-52x-\frac{38x-684}{5}\right)19\)
\(< =>55x-1441=1631-52x-\frac{38x-684}{5}\)
\(< =>3072-107x=\frac{38x-684}{5}\)
\(< =>\left(3072-107x\right)5=38x-684\)
\(< =>15360-535x-38x-684=0\)
\(< =>14676=573x< =>x=\frac{14676}{573}=\frac{4892}{191}\)
nghệm xấu thế
\(\frac{8\left(x+22\right)}{45}-\frac{7x+149+\frac{6\left(x+12\right)}{5}}{9}=\frac{x+35+\frac{2\left(x+50\right)}{9}}{5}\)
\(< =>\frac{8x+176}{45}-\frac{41x+817}{45}=\frac{11x+415}{45}\)
\(< =>993-33x-11x-415=0\)
\(< =>578=44x< =>x=\frac{289}{22}\)
Bài 1:
b) Phương trình đã cho tương đương với phương trình:
\(\frac{8\left(x+22\right)-55\left(7x+149\right)-6\left(x+12\right)}{45}=\frac{9\left(x+35\right)+2\left(x+50\right)}{45}\)
\(\Leftrightarrow44x=-1056\)
\(\Leftrightarrow x=-24\)
Vậy x=-24 là nghiệm của phương trình
c) Phương trình đã cho tương đương với phương trình:
\(\frac{3x+6}{70}-\frac{x+4}{24}=\frac{32x+19}{60}+\frac{2}{3}\)
\(\Leftrightarrow12\left(3x+6\right)-35\left(x+4\right)=14\left(32x+19\right)+560\)
\(\Leftrightarrow-447x=894\)
\(\Leftrightarrow x=-2\)
Vậy x=-2 là nghiệm của phương trình
BÀI 5 : CHO
E=\(\frac{x^2+6x+9}{x^3+3x^2-27x+27}\). \(\left(\frac{x^2+6x+9}{x^3+3x^2-27x+27}+\frac{2}{3x}:\left(\frac{1}{x}+\frac{1}{3}\right)^2\right)\)
F=\(\frac{3+x}{3-x}\) .\(\frac{x^2-6x+9}{9x^2}\).\(\left(\frac{3}{3-x}-\frac{9}{27+x^3}.\frac{x^2-3x+9}{3-x}\right)\)
a, RÚT GỌN E VÀ F
Tìm x biết
a) (8-5x).(x+2)+4.(x-2).(x+1)+2.(x-2).(x+2)=0
b)\(\left(-\frac{2}{5}+x\right):\frac{7}{9}+\left(-\frac{3}{5}+\frac{5}{6}\right):\frac{7}{9}=0\)
c)\(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=1\frac{2003}{2004}\)
Tìm x, biết: \(\frac{-1}{2}.\left(3x+5\right)-\frac{2}{9}.\left(9-6x\right)=\frac{3}{5}.\left(x-10\right)-3\)
Bài 1 : rút gọn các phân thức sau :
a)\(\frac{7x-14y}{x^2-4y^2}\) b)\(\frac{x^3+8}{x^4-25}:\frac{x^2-2x+4}{x^2+5}\) c)\(\frac{x^2+7x}{x^2-9}.\frac{x^2+6x+9}{x^2-49}\)
Bài 2: Thực hiện các phép phép tính sau :
a)\(\frac{3x+5}{4x^3y}-\frac{5-15x}{4x^3y}\) b) \(\frac{4x+7}{2x+2}-\frac{3x+6}{2x+2}\) c) \(\frac{18}{\left(x-3\right)\left(x^2-9\right)}-\frac{3}{x^2-6x+9}-\frac{x}{x^2-9}\)