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a/ S=\(\left(\frac{x}{\left(x+6\right)\left(x-6\right)}-\frac{x-6}{x\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}-\frac{x}{x-6}\)
S=\(\frac{x^2-\left(x-6\right)^2}{x\left(x+6\right)\left(x-6\right)}.\frac{x\left(x+6\right)}{2x-6}-\frac{x}{x-6}\)=\(\frac{\left(x-x+6\right)\left(x+x-6\right)}{\left(x-6\right)\left(2x-6\right)}-\frac{x}{x-6}\)
= \(\frac{6\left(2x-6\right)}{\left(x-6\right)\left(2x-6\right)}-\frac{x}{x-6}\)= \(\frac{6}{\left(x-6\right)}-\frac{x}{x-6}\)\(\frac{6-x}{x-6}=-1\)
b/ S luôn =-1 với mọi x
\(a,\frac{7}{x}-\frac{x}{x+6}+\frac{36}{x^2-6x}\)
\(=\frac{7}{x}-\frac{x}{x+6}+\frac{36}{x\left(x-6\right)}\)
\(=\frac{7\left(x-6\right)\left(x+6\right)-x\left(x-6\right)+36\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)}\)
\(=\frac{7\left(x^2-6\right)-x^2+6x+36x+216}{x\left(x^2-6\right)}\)
\(=\frac{7x^2-42-x^2+6x+36x+216}{x\left(x^2-6\right)}\)
\(=\frac{6x^2+42x+216}{x\left(x^2-6\right)}\)
\(=\frac{6\left(x^2+7x+36\right)}{x\left(x^2-6\right)}\)
Đề sai nhé, phải là như này nè :
\(b,\frac{1}{x^2-x+1}-\frac{1}{x^2+x+1}-\frac{2x}{x^4-x^2+1}+\frac{4x^3}{x^8-x^4+1}\)
\(=\frac{x^2+x+1-\left(x^2-x+1\right)}{\left(x^2-x+1\right)\left(x^2+x+1\right)}\)\(-\frac{2x}{x^4-x^2+1}+\frac{4x^3}{x^8-x^4+1}\)
\(=\frac{x^2+x+1-x^2+x-1}{x^4+x^2+1}\)\(-\frac{2x}{x^4-x^2+1}+\frac{4x^3}{x^8-x^4+1}\)
\(=\frac{2x}{x^4+x^2+1}-\frac{2x}{x^4-x^2+1}+\frac{4x^3}{x^8-x^4+1}\)
\(=\frac{2x\left(x^4-x^2+1\right)-2x\left(x^4+x^2+1\right)}{\left(x^4+x^2+1\right)\left(x^4-x^2+1\right)}+\frac{4x^3}{x^8-x^4+1}\)
\(=\frac{2x^5-2x^3+2x-2x^5-2x^3-2x}{x^8-x^4+1}+\frac{4x^3}{x^8-x^4+1}\)
\(=-\frac{4x^3}{x^8-x^4+1}+\frac{4x^3}{x^8-x^4+1}=0\)
Ta có:\(\left(\frac{6}{x^2-6x}+\frac{1}{x+6}\right):\frac{x^2+36}{x^2-36}\)
\(=\left(\frac{6\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)}+\frac{x\left(x-6\right)}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x^2-6^2}{x^2+36}\)
\(=\left(\frac{6x+36+x^2-6x}{x\left(x-6\right)\left(x+6\right)}\right).\frac{\left(x-6\right)\left(x+6\right)}{x^2+36}\)
\(=\frac{x^2+36}{x\left(x-6\right)\left(x+6\right)}.\frac{\left(x-6\right)\left(x+6\right)}{x^2+36}\)
\(=\frac{1}{x}\)
Kiểm tra đi bạn phải là \(\frac{1}{x}\)
NÓI LUÔN LÀ RÚT GỌN C/M nghe nặng nề quá
ĐK tồn tại \(x\ne\) {-6,0,6}
\(A=\left(\frac{36+6x+x^2-6}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x^2+36}{\left(x-6\right)\left(x+6\right)}\) Bẫy rồi
đây là dấu nhân hả bạn???