Question

Thực hiện phép tính

x+1 / x -2    -   x-1 / x+2     -  7x+2 / x^2 -4

3x+1 / x^2 - 2x +1   -  1 / x +1    +   x+3 / 1 -x^2

1 / x(x + 1)   +  1/ (x + 1)(x +2)  + ........+ 1/(x + 2015)(x + 2016) 

giải chi tiết giùm nha

Answer 1

câu b nè

\(\frac{3x+1}{\left(x-1\right)^2}-\frac{1}{x+1}-\frac{x+3}{x^2-1}\)

=\(\frac{\left(3x+1\right)\left(x+1\right)}{\left(x-1\right)^2\left(x+1\right)}-\frac{\left(x-1\right)^2}{\left(x-1\right)^2\left(x+1\right)}-\frac{\left(x+3\right)\left(x-1\right)}{\left(x-1\right)^2\left(x+1\right)}\)

=\(\frac{\left(3x^2+x+3x+1\right)-\left(x^2-2x+1\right)-\left(x^2-x-3+3x\right)}{\left(x-1\right)^2\left(x+1\right)}\)

=\(\frac{3x^2+4x+1-x^2+2x-1-x^2-2x+3}{\left(x-1\right)^2\left(x+1\right)}=\frac{x^2+4x+3}{\left(x+1\right)\left(x-1^2\right)}\)

=\(\frac{\left(x+1\right)\left(x+3\right)}{\left(x+1\right)\left(x-1\right)^2}=\frac{x+3}{\left(x-1\right)^2}\)