Phân thức đại số
Các câu hỏi tương tự
Bài 1: Tìm x để các phân thức = 0
a) \(\dfrac{x^{2^{ }}+8x+7}{x^2-49}\)
b) \(\dfrac{x^{2^{ }}-100}{x^2+20+100}\)
c)\(\dfrac{x^2-5x+6}{x^2-4}\)
Giải các phương trình sau :
1.dfrac{14}{3x-12}-dfrac{2+x}{x-4}dfrac{3}{8-2x}-dfrac{5}{6}
2.dfrac{12}{1-9x^2}dfrac{1-3x}{1+3x}-dfrac{1+3x}{1-3x}
3.dfrac{x+5}{x^2-5x}-dfrac{x+25}{2x^2-50}dfrac{x-5}{2x^2+10x}
4.dfrac{6x_{ }+1}{x^2-7x+10}+dfrac{5}{x-2}dfrac{3}{x-5}
5.dfrac{2}{x^2-4}-dfrac{x-1}{xleft(x-2right)}+dfrac{x-4}{xleft(x+2right)}0
6.dfrac{2}{x+2}-dfrac{2x^2+16}{x^3+8}dfrac{5}{x^2-2x+4}
Đọc tiếp
Giải các phương trình sau :
1.\(\dfrac{14}{3x-12}-\dfrac{2+x}{x-4}=\dfrac{3}{8-2x}-\dfrac{5}{6}\)
2.\(\dfrac{12}{1-9x^2}=\dfrac{1-3x}{1+3x}-\dfrac{1+3x}{1-3x}\)
3.\(\dfrac{x+5}{x^2-5x}-\dfrac{x+25}{2x^2-50}=\dfrac{x-5}{2x^2+10x}\)
4.\(\dfrac{6x_{ }+1}{x^2-7x+10}+\dfrac{5}{x-2}=\dfrac{3}{x-5}\)
5.\(\dfrac{2}{x^2-4}-\dfrac{x-1}{x\left(x-2\right)}+\dfrac{x-4}{x\left(x+2\right)}=0\)
6.\(\dfrac{2}{x+2}-\dfrac{2x^2+16}{x^3+8}=\dfrac{5}{x^2-2x+4}\)
a) \(\dfrac{1}{x^2+x}+\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}\)
b) \(\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}+\dfrac{1}{x^2+9x+20}\)
CMR \(\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1}{x\left(x+1\right)}\)
áp dụng kết quả bài toán trên, tính:
\(\dfrac{1}{^{^{ }}x^2+x}+\dfrac{1}{x^2+3\text{x}+2}+\dfrac{1}{x^2+6\text{x}+6}+\dfrac{1}{x^2+7\text{x}+12}+\dfrac{1}{x^2+9\text{x}+20}+\dfrac{1}{x+5}_{ }\)
giải phương trình
a.\(\left(2x-3\right)^2=\left(2x-3\right)\left(x+1\right)\)
b.\(x\left(2x-9\right)=3x\left(x-5\right)\)
c.\(3x-15=2x\left(x-5\right)\)
d.\(\dfrac{5-x}{2}=\dfrac{3x-4}{6}\)
e.\(\dfrac{3x+2}{2}-\dfrac{3x+1}{6}=2x+\dfrac{5}{3}\)
a) dfrac{2a-1}{2a+1}-dfrac{2a-3}{2a-1}
b) dfrac{1}{x+1}-dfrac{1}{x-1}-dfrac{2x^2}{1-x^2}
c) dfrac{x+1}{left(x+2right)^2}-dfrac{1}{x+2}-dfrac{1}{1-x^2}
d) dfrac{x-5}{x^2+3x}+dfrac{6}{x+3}
e) x+2+dfrac{3}{x-2}
g) dfrac{4-x}{x^2-4x}+dfrac{3}{x}+dfrac{-2}{x+1}
h) dfrac{x+1}{x-3}+dfrac{-2x^2+2x}{x^2-9}+dfrac{x-1}{x+3}
i) dfrac{x}{x^2-4x}-dfrac{3}{5x}
k) dfrac{1}{xy-x^2}-dfrac{1}{y^2-xy}
Đọc tiếp
a) \(\dfrac{2a-1}{2a+1}-\dfrac{2a-3}{2a-1}\)
b) \(\dfrac{1}{x+1}-\dfrac{1}{x-1}-\dfrac{2x^2}{1-x^2}\)
c) \(\dfrac{x+1}{\left(x+2\right)^2}-\dfrac{1}{x+2}-\dfrac{1}{1-x^2}\)
d) \(\dfrac{x-5}{x^2+3x}+\dfrac{6}{x+3}\)
e) \(x+2+\dfrac{3}{x-2}\)
g) \(\dfrac{4-x}{x^2-4x}+\dfrac{3}{x}+\dfrac{-2}{x+1}\)
h) \(\dfrac{x+1}{x-3}+\dfrac{-2x^2+2x}{x^2-9}+\dfrac{x-1}{x+3}\)
i) \(\dfrac{x}{x^2-4x}-\dfrac{3}{5x}\)
k) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
Thực hiện phép tính:
1. dfrac{x^2}{x+1}+dfrac{2x}{x^2-1}-dfrac{1}{1-x}+1
2. dfrac{1}{x^3-x}-dfrac{1}{left(x-1right)x}+dfrac{2}{x^2-1}
3. dfrac{y}{xy-5y^2}-dfrac{15y-25x}{y^2-25x^2}
4. dfrac{4-2x+x^2}{2+x}-2-x
5. dfrac{2x^3-2y^3}{3x+3y}:dfrac{2x^2+2xy+y^2}{x^2+2xy+y^2}
6. left(dfrac{1+x}{1-x}-dfrac{1-x}{1+x}right)left(dfrac{3}{4x}+dfrac{x}{4}-xright)
Đọc tiếp
Thực hiện phép tính:
1. \(\dfrac{x^2}{x+1}+\dfrac{2x}{x^2-1}-\dfrac{1}{1-x}+1\)
2. \(\dfrac{1}{x^3-x}-\dfrac{1}{\left(x-1\right)x}+\dfrac{2}{x^2-1}\)
3. \(\dfrac{y}{xy-5y^2}-\dfrac{15y-25x}{y^2-25x^2}\)
4. \(\dfrac{4-2x+x^2}{2+x}-2-x\)
5. \(\dfrac{2x^3-2y^3}{3x+3y}:\dfrac{2x^2+2xy+y^2}{x^2+2xy+y^2}\)
6. \(\left(\dfrac{1+x}{1-x}-\dfrac{1-x}{1+x}\right)\left(\dfrac{3}{4x}+\dfrac{x}{4}-x\right)\)
Bài 1: Thực hiện phép tính
a, dfrac{8}{left(x^2+3right)left(x^2-1right)}+dfrac{2}{x^2+3}+dfrac{1}{x+1}
b, dfrac{x+y}{2left(x-yright)}-dfrac{x-y}{2left(x+yright)}+dfrac{2y^2}{x^2-y^2}
c, dfrac{x-1}{x^3}-dfrac{x+1}{x^3-x^2}+dfrac{3}{x^3-2x^2+x}
d, dfrac{xy}{ab}+dfrac{left(x-aright)left(y-aright)}{aleft(a-bright)}-dfrac{left(x-bright)left(y-bright)}{bleft(a-bright)}
e, dfrac{x^3}{x-1}-dfrac{x^2}{x+1}-dfrac{1}{x-1}+dfrac{1}{x+1}
f, dfrac{x^3+x^2-2x-20}{x^2-4}-dfrac{5}{x+2}+dfrac{3}{x-2}
g, le...
Đọc tiếp
Bài 1: Thực hiện phép tính
a, \(\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}\)+\(\dfrac{2}{x^2+3}\)+\(\dfrac{1}{x+1}\)
b, \(\dfrac{x+y}{2\left(x-y\right)}\)-\(\dfrac{x-y}{2\left(x+y\right)}\)+\(\dfrac{2y^2}{x^2-y^2}\)
c, \(\dfrac{x-1}{x^3}\)-\(\dfrac{x+1}{x^3-x^2}\)+\(\dfrac{3}{x^3-2x^2+x}\)
d, \(\dfrac{xy}{ab}\)+\(\dfrac{\left(x-a\right)\left(y-a\right)}{a\left(a-b\right)}\)-\(\dfrac{\left(x-b\right)\left(y-b\right)}{b\left(a-b\right)}\)
e, \(\dfrac{x^3}{x-1}\)-\(\dfrac{x^2}{x+1}\)-\(\dfrac{1}{x-1}\)+\(\dfrac{1}{x+1}\)
f, \(\dfrac{x^3+x^2-2x-20}{x^2-4}\)-\(\dfrac{5}{x+2}\)+\(\dfrac{3}{x-2}\)
g, \(\left\{\dfrac{x-y}{x+y}+\dfrac{x+y}{x-y}\right\}\).\(\left\{\dfrac{x^2+y^2}{2xy}\right\}\).\(\dfrac{xy}{x^2+y^2}\)
h, \(\dfrac{1}{\left(a-b\right)\left(b-c\right)}\)+\(\dfrac{1}{\left(b-c\right)\left(c-a\right)}\)+\(\dfrac{1}{\left(c-a\right)\left(a-b\right)}\)
i, \(\dfrac{\left[a^2-\left(b+c\right)^2\right]\left(a+b-c\right)}{\left(a+b+c\right)\left(a^2+c^2-2ac-b^2\right)}\)
k, \(\left[\dfrac{x^2-y^2}{xy}-\dfrac{1}{x+y}\left\{\dfrac{x^2}{y}-\dfrac{y^2}{x}\right\}\right]\):\(\dfrac{x-y}{x}\)
Bài 2: Rút gọn các phân thức:
a, \(\dfrac{25x^2-20x+4}{25x^2-4}\)
b, \(\dfrac{5x^2+10xy+5y^2}{3x^3+3y^3}\)
c, \(\dfrac{x^2-1}{x^3-x^2-x+1}\)
d, \(\dfrac{x^3+x^2-4x-4}{x^4-16}\)
e, \(\dfrac{4x^4-20x^3+13x^2+30x+9}{\left(4x^2-1\right)^2}\)
Bài 3: Rút gọn rồi tính giá trị các biểu thức:
a, \(\dfrac{a^2+b^2-c^2+2ab}{a^2-b^2+c^2+2ac}\) với a = 4, b = -5, c = 6
b, \(\dfrac{16x^2-40xy}{8x^2-24xy}\) với \(\dfrac{x}{y}\) = \(\dfrac{10}{3}\)
c, \(\dfrac{\dfrac{x^2+xy+y^2}{x+y}-\dfrac{x^2-xy+y^2}{x-y}}{x-y-\dfrac{x^2}{x+y}}\) với x = 9, y = 10
Bài 4: Tìm các giá trị nguyên của biến số x để biểu thức đã cho cũng có giá trị nguyên:
a, \(\dfrac{x^3-x^2+2}{x-1}\)
b, \(\dfrac{x^3-2x^2+4}{x-2}\)
c, \(\dfrac{2x^3+x^2+2x+2}{2x+1}\)
d, \(\dfrac{3x^3-7x^2+11x-1}{3x-1}\)
e, \(\dfrac{x^4-16}{x^4-4x^3+8x^2-16x+16}\)
Cho x, y , x là các số thực thỏa mãn: \(\dfrac{x^4}{a}+\dfrac{y^4}{b}=\dfrac{x^2+y^2}{a+b};x^2+y^2=1\)
Chứng minh:\(\dfrac{x^{2006}}{a^{1003}}+\dfrac{y^{2006}}{b^{1003}}=\dfrac{2}{\left(a+b\right)^{1003}}\)