Question

RÚT GỌN CÁC BIỂU thức

●1) 1/1-x + 1/1+x + 2/1+x^2 + 4/1+x^4 + 8/1+x^8

●2)1/x^2+x + 1/x^2+3x+2 + 1/x^2+5x+6 + 1/x^2+7x+12

GIÚP MK VỚI. mk đang rất Cần :(((

Answer 1

1:

\(=\dfrac{1+x+1-x}{1-x^2}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}\)

\(=\dfrac{2+2x^2+2-2x^2}{1-x^4}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}\)

\(=\dfrac{4+4x^4+4-4x^4}{1-x^8}+\dfrac{8}{1+x^8}\)

\(=\dfrac{8+8x^8+8-8x^8}{1-x^{16}}=\dfrac{16}{1-x^{16}}\)

2: \(=\dfrac{1}{x}-\dfrac{1}{x+1}+\dfrac{1}{x+1}-\dfrac{1}{x+2}+\dfrac{1}{x+2}-\dfrac{1}{x+3}+\dfrac{1}{x+3}-\dfrac{1}{x+4}\)

=(x+4-x)/x(x+4)=4/x(x+4)