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11 tháng 12 2020

\(\left(\frac{4}{x-4}-\frac{4}{x+4}\right)\times\frac{x^2+8x+16}{32}\)

ĐKXĐ : \(x\ne\pm4\)

\(=\left(\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}-\frac{4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}\right)\times\frac{\left(x+4\right)^2}{32}\)

\(=\left(\frac{4x+16-4x+16}{\left(x-4\right)\left(x+4\right)}\right)\times\frac{\left(x+4\right)^2}{32}\)

\(=\frac{32}{\left(x-4\right)\left(x+4\right)}\times\frac{\left(x+4\right)^2}{32}\)

\(=\frac{x+4}{x-4}\)

11 tháng 12 2020

\(\left(\frac{4}{x-4}-\frac{4}{x+4}\right).\frac{x^2+8x+16}{32}\)

\(=\left(\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}-\frac{4\left(x-4\right)}{\left(x+4\right)\left(x-4\right)}\right).\frac{\left(x+4\right)^2}{32}\)

\(=\frac{4x+16-4x+16}{\left(x-4\right)\left(x+4\right)}.\frac{\left(x+4\right)^2}{32}=\frac{32}{\left(x-4\right)\left(x+4\right)}.\frac{\left(x+4\right)^2}{32}=\frac{x+4}{x-4}\)

10 tháng 11 2016

\(A=x^5+2x^4+4x^3+8x^2+16x-2x^4-4x^3-8x^2-16x-32\)

\(=x^5-32\)(1)

Thay x=3 vào (1) ta được:

\(A=3^5-32=243-32=211\)

23 tháng 7 2017

\(\left(x-2\right)\left(x^2-2x+1\right)\left(x+2\right)\left(x^2+2x+4\right)\)

\(=\left[\left(x-2\right)\left(x^2+2x+4\right)\right]\left[\left(x+2\right)\left(x^2-2x+4\right)\right]\)

\(=\left(x^3-8\right)\left(x^3+8\right)\)

\(=x^6-64\)

1 tháng 7 2018

\(\left(x-2\right)\left(x^2-2x+4\right)\left(x+2\right)\left(x^2+2x+4\right)\)

\(=\left(x-2\right)\left(x^2+2x+4\right)\left(x+2\right)\left(x^2-2x+4\right)\)

\(=\left(x^3-8\right)\left(x^3+8\right)\)

\(=x^6+64\)

30 tháng 7 2021

\(\frac{4}{x+2}+\frac{3}{x-2}+\frac{-5x-2}{x^2-4}\)ĐK : \(x\ne\pm2\)

\(=\frac{4\left(x-2\right)+3\left(x+2\right)-5x-2}{\left(x+2\right)\left(x-2\right)}=\frac{4x-8+3x+6-5x-2}{\left(x+2\right)\left(x-2\right)}\)

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

9 tháng 11 2018

\(a,\left(2x^2-3x\right)\left(x-4\right)=2x^3-8x^2-3x^2+12x=2x^3-11x^2+12x\)

\(b,\left(x-1\right)\left(x^4-x^3+x^2-x+1\right)\)

\(=x^5-x^4+x^3-x^2+x-x^4+x^3-x^2+x-1\)

\(=x^5-2x^4+2x^3-2x^2+2x-1\)