\(\frac{1}{x-1}-\frac{1}{x+1}-\frac{1}{x^2+1}-\frac{1}{x^4+1}-\frac{1}{x^8+1}-\frac{1}{x^{16}+1}\)thực hiện phép tính
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Thực hiện phép tính :
\(\frac{2}{1-x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}+\frac{32}{1+x^{32}}\)
khó quá làm sao mà trả lời đc
tự đầu mình vắt óc mà suy nghĩ
Xem thêm câu trả lời
thực hiện phép tính \(A=\frac{1}{x-1}-\frac{1}{x-1}-\frac{2}{x^2+1}-\frac{4}{x^4+1}-\frac{8}{x^8+1}-\frac{16}{x^{16}+1}\)
1 thực hiện phép tính
a,\(\frac{x+3}{x+1}-\frac{2x-1}{x-1}-\frac{x-3}{x^2-1}\)
b, \(\frac{1}{x^2+x+1}+\frac{1}{x^2-x}+\frac{2x}{1-x^3}\)
c, \(\frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{x^2+1}-\frac{4}{x^4+1}-\frac{8}{x^8+1}-\frac{16}{x^{16}+1}\)
thực hiên phép tính:
\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{1}{1+x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
Bài 1: Thưch hiện phép tính:
\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
= 1+x+1--x/1-x^2 +2/1+x^2+....+16/1+x^26
= 2/1-x^2+2/1+x^2+....+16/1+x^16
= ........
= 16/1-x^16 + 16/1+x^16
= 16+16x^16+16-16x^16/1-x^32
= 32/1-x^32
k mk nha
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ĐKXĐ: \(x\ne\pm1\)
\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{2}{1-x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{4}{1-x^4}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{8}{1-x^8}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{16}{1-x^{16}}+\frac{16}{1+x^{16}}\)
\(=\frac{32}{1-x^{32}}\)
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thực hiện phép tính: \(\frac{1}{1-x}\)+\(\frac{1}{1+x}\)+\(\frac{2}{1+x^2}\)+\(\frac{4}{1+x^4}\)+\(\frac{8}{1+x^8}\)+\(\frac{16}{1+x^{16}}\)
Ta có:\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{1+x}{\left(1-x\right)\left(1+x\right)}+\frac{1-x}{\left(1-x\right)\left(1+x\right)}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)\(=\frac{2}{\left(1-x\right)\left(1+x\right)}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{2}{1-x^2}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{2\left(1+x^2\right)}{\left(1-x^2\right)\left(1+x^2\right)}+\frac{2\left(1-x^2\right)}{\left(1-x^2\right)\left(1+x^2\right)}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{2+2x^2}{\left(1-x^2\right)\left(1+x^2\right)}+\frac{2-2x^2}{\left(1-x^2\right)\left(1+x^2\right)}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{2+2}{\left(1-x^2\right)\left(1+x^2\right)}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{4}{1-x^4}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{4\left(1+x^4\right)}{\left(1-x^4\right)\left(1+x^4\right)}+\frac{4\left(1-x^4\right)}{\left(1-x^4\right)\left(1+x^4\right)}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{4+4x^4}{\left(1-x^4\right)\left(1+x^4\right)}+\frac{4-4x^4}{\left(1-x^4\right)\left(1+x^4\right)}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{4+4}{\left(1-x^4\right)\left(1+x^4\right)}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{8}{1-x^8}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
\(=\frac{8\left(1+x^8\right)}{\left(1-x^8\right)\left(1+x^8\right)}+\frac{8\left(1-x^8\right)}{\left(1-x^8\right)\left(1+x^8\right)}+\frac{16}{1+x^{16}}\)
\(=\frac{8+8x^8}{\left(1-x^8\right)\left(1+x^8\right)}+\frac{8-8x^8}{\left(1-x^8\right)\left(1+x^8\right)}+\frac{16}{1+x^{16}}\)
\(=\frac{8+8}{\left(1-x^8\right)\left(1+x^8\right)}+\frac{16}{1+x^{16}}\)
\(=\frac{16}{1-x^{16}}+\frac{16}{1+x^{16}}\)
\(=\frac{16\left(1+x^{16}\right)}{\left(1-x^{16}\right)\left(1+x^{16}\right)}+\frac{16\left(1-x^{16}\right)}{\left(1-x^{16}\right)\left(1+x^{16}\right)}\)
\(=\frac{16+16}{\left(1-x^{16}\right)\left(1+x^{16}\right)}\)
\(=\frac{32}{1-x^{32}}\)
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Thực hiện phép tính :a)frac{x^2}{left(x-yright)^2left(x+yright)}-frac{2xy^2}{x^4-2x^2y^2+y^4}+frac{y^2}{left(x^2-y^2right)left(x+yright)} b)frac{1}{x-1}-frac{1}{x+1}-frac{2}{x^2+1}-frac{4}{x^4+1}-frac{8}{x^{8+1}}-frac{16}{x^{16}+1}c)frac{1}{x^2+6x+9}+frac{1}{6x-x^2-9}+frac{x}{x^2-9}d)frac{a}{x^2+ax}+frac{a}{x^2+3ax+2a^2}+frac{a}{x^2+5ax+6a^2}+....+frac{a}{x^2+19ax+90a^2}+frac{1}{x+10a}
Đọc tiếp
Thực hiện phép tính :
a)\(\frac{x^2}{\left(x-y\right)^2\left(x+y\right)}-\frac{2xy^2}{x^4-2x^2y^2+y^4}+\frac{y^2}{\left(x^2-y^2\right)\left(x+y\right)}\)
b)\(\frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{x^2+1}-\frac{4}{x^4+1}-\frac{8}{x^{8+1}}-\frac{16}{x^{16}+1}\)
c)\(\frac{1}{x^2+6x+9}+\frac{1}{6x-x^2-9}+\frac{x}{x^2-9}\)
d)\(\frac{a}{x^2+ax}+\frac{a}{x^2+3ax+2a^2}+\frac{a}{x^2+5ax+6a^2}+....+\frac{a}{x^2+19ax+90a^2}+\frac{1}{x+10a}\)
Bái 3. Thực hiện phép tính
A=\(\frac{4x^3}{x^4-16}-\frac{1}{x+2}+\frac{2x}{x^2+4}-\frac{1}{x-2}\\ \)
B= \(\frac{1}{x-1}+\frac{2x+3}{\left(x+1\right)^2}-\frac{1}{\left(x+1\right)^2}-\frac{3x-2}{x^2-1}\)
C= \(\left(1+\frac{1}{x}\right)\left(1+\frac{1}{x+1}\right)\left(1+\frac{1}{x+2}\right)...\left(1+\frac{1}{x+9}\right)\)
8,Thực hiện phép tínha,frac{5x^2-y^2}{xy}-frac{3x-2y}{y}b,frac{3}{2x+6}-frac{x-6}{2x^2+6x}c,frac{2x}{x^2+2xy}+frac{y}{xy-2y^2}+frac{4}{x^2-4y^2} d,frac{1}{x-y}+frac{3xy}{y^3-x^3}+frac{x-y}{x^2+xy+y^2} e,frac{2x+y}{2x^2-xy}+frac{16x}{y^2-4x^2}+frac{2x-y}{2x^2+xy} f,frac{1}{1-x}+frac{1}{1+x}+frac{2}{1+x^2}+frac{4}{1+x^4}+frac{8}{1+x^8}+frac{16}{1+x^{16}}
Đọc tiếp
8,Thực hiện phép tính
a,\(\frac{5x^2-y^2}{xy}-\frac{3x-2y}{y}\)
b,\(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}\)
c,\(\frac{2x}{x^2+2xy}+\frac{y}{xy-2y^2}+\frac{4}{x^2-4y^2}\)
d,\(\frac{1}{x-y}+\frac{3xy}{y^3-x^3}+\frac{x-y}{x^2+xy+y^2}\)
e,\(\frac{2x+y}{2x^2-xy}+\frac{16x}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}\)
f,\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)