\(\left(\frac{4}{3}x^{n+1}-\frac{1}{2}y^n\right).2xy-\left(\frac{2}{3}x^{n+1}-\frac{5}{6}y^n\right).7xy\)
\(\left(\frac{3}{4}x^{n+1}-\frac{1}{2}y^n\right).2xy-\left(\frac{2}{3}x^{n+1}-\frac{5}{6}y^n\right).7xy\)
Rút gọn:
a) 5(3xn-1-yn-1)-3(xn+1+5yn-1)+4(-xn+1+2yn-1)
b) \(\left(\frac{3}{4}x^{n+1}-\frac{1}{2}y^n\right)2xy-\left(\frac{2}{3}x^{n+1}-\frac{5}{6}y^n\right).7xy\)
Cho \(n^4+\frac{1}{4}=\left(\left(n-1\right)n+\frac{1}{2}\right)\left(\left(n+1\right)n+\frac{1}{2}\right)\)
Thu gọn phân thức:
\(\frac{\left(1^4+\frac{1}{4}\right)\left(3^4+\frac{1}{4}\right)\left(5^4+\frac{1}{4}\right)...\left(13^4+\frac{1}{4}\right)}{\left(2^4+\frac{1}{4}\right)\left(4^4+\frac{1}{4}\right)\left(6^4+\frac{1}{4}\right)...\left(14^4+\frac{1}{4}\right)}\)
Rút gọn:
\(\frac{1}{\left(x+y\right)^3}\cdot\left(\frac{1}{x^3}+\frac{1}{y^3}\right)+\frac{3}{\left(x+y\right)^4}\cdot\left(\frac{1}{x^2}+\frac{1}{y^2}\right)+\frac{6}{\left(x+y\right)^5}\cdot\left(\frac{1}{x}+\frac{1}{y}\right)\)
1. Tìm giá trị của x để các phân thức sau bằng 0
a. \(\frac{x^4+x^3+x+1}{x^4-x^3+2x^2-x+1}\)
b. \(\frac{x^4-5x^2+4}{x^4-10x^2+9}\)
2. Rút gọn các phân thức:
a. \(\frac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\) b. \(\frac{\left(x-y\right)^3-3xy\left(x+y\right)+y^{^3}}{x-6y}\)
3. Rút gọn các phân thức với n là số tự nhiên
a. \(\frac{\left(n+1\right)!}{n!\left(n+2\right)}\) b. \(\frac{n!}{\left(n+1\right)!-n!}\) c. \(\frac{\left(n+1\right)!-\left(n+2\right)!}{\left(n+1\right)!+\left(n+2\right)!}\)
Làm được câu nào thì giúp mình với!!!
1. Rút gọn: \(\left(\frac{y^2-yz-z^2}{x}+\frac{x^2}{y+z}-\frac{3}{\frac{1}{y}+\frac{1}{z}}\right).\frac{\frac{2}{y}+\frac{2}{z}}{\frac{1}{yz}+\frac{1}{xy}+\frac{1}{xz}+\left(x+y+z\right)^2}\)
2. Tính giá trị của biểu thức:
\(A=\left(\frac{m-n}{p}+\frac{n-p}{m}+\frac{p-m}{n}\right)\left(\frac{p}{m-n}+\frac{m}{n-p}+\frac{n}{p-m}\right)\)biết \(m+n+p=0\)
Giải phương trình:
1.\(\frac{x-5}{x-5}+\frac{x-6}{x-5}+\frac{x-7}{x-5}+...+\frac{1}{x-5}=4\left(x\in N\right)\)
2.\(\frac{1}{x^2+3x+2}+\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+...+\frac{1}{x^2+15x+56}=\frac{1}{14}\)
3.\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{x\left(x+2\right)}\right)=\frac{31}{16}\left(x\in N\right)\)
4.\(8\left(x^2+\frac{1}{x^2}\right)-34\left(x+\frac{1}{x}\right)+51=0\)
5.\(6x^4-5x^3-38x^2-5x+6=0\)
CMR: \(\frac{1}{\left(x+y\right)^3}.\left(\frac{1}{x^3}+\frac{1}{y^3}\right)+\frac{3}{\left(x+y\right)^4}.\left(\frac{1}{x^2}+\frac{1}{y^2}\right)+\frac{6}{\left(x+y\right)^5}.\left(\frac{1}{x}+\frac{1}{y}\right)=\frac{1}{x^3y^3}\)