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\(A=\left(\frac{6x+1}{x^2-6x}+\frac{6x-1}{x^2+6x}\right)\times\frac{x^2-36}{12x^2+12}\)
\(A=\left[\frac{6x+1}{x\left(x-6\right)}+\frac{6x-1}{x\left(x+6\right)}\right]\times\frac{\left(x+6\right)\left(x-6\right)}{12\left(x^2+1\right)}\)
\(A=\frac{6x^2+36x+x+6+6x^2-36x-x+6}{x}\times\frac{1}{12\left(x^2+1\right)}\)
\(A=\frac{12\left(x^2+1\right)}{x}\times\frac{1}{12\left(x^2+1\right)}=\frac{1}{x}\)
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 \(\frac{1}{x}\)
Lời giải:
a) ĐKXĐ: \(\left\{\begin{matrix} x^2-6x\neq 0\\ x^2+6x\neq 0\\ x^2+1\neq 0\end{matrix}\right.\Leftrightarrow x\neq 0; x\neq \pm 6\)
b)
\(A=\left(\frac{6x+1}{x^2-6x}+\frac{6x-1}{x^2+6x}\right).\frac{x^2-36}{x^2+1}=\frac{(6x+1)(x+6)+(6x-1)(x-6)}{x(x-6)(x+6)}.\frac{x^2-36}{x^2+1}\)
\(=\frac{6x^2+37x+6+6x^2-37x+6}{x(x-6)(x+6)}.\frac{(x-6)(x+6)}{x^2+1}=\frac{12(x^2+1)}{x(x-6)(x+6)}.\frac{(x-6)(x+6)}{x^2+1}=\frac{12}{x}\)
\(1,ĐK:x\ne0;x\ne\pm6\)
\(A=\left[\frac{6x+1}{x\left(x-6\right)}+\frac{6x-1}{x\left(x+6\right)}\right].\frac{\left(x+6\right)\left(x-6\right)}{12\left(x^2+1\right)}\)
\(=\frac{6x^2+36x+x+6+6x^2-36x-x+6}{x}.\frac{1}{12\left(x^2+1\right)}\)
\(=\frac{12\left(x^2+1\right)}{x}.\frac{1}{12\left(x^2+1\right)}=\frac{1}{x}\)
\(2,A=\frac{1}{x}=\frac{1}{\frac{1}{\sqrt{9+4\sqrt{5}}}}=\sqrt{9+4\sqrt{5}}\)
Cho tam giác ABC vuông tại B có góc B1=B2 ; Â=60o, kẻ BH vuông góc với AC (H thuộc AC). Qua B kẻ đường thẳng d song song với AC.
a) Tính góc ABH.
b) Chứng minh đường thẳng d vuông góc với BH.
\(VT=\left[\frac{6x+1}{x\left(x-6\right)}+\frac{6x-1}{x\left(x+6\right)}\right]:\frac{x^2+1}{\left(x-6\right)\left(x+6\right)}=\)
\(=\left[\frac{\left(6x+1\right)\left(x+6\right)+\left(6x-1\right)\left(x-6\right)}{x\left(x-6\right)\left(x+6\right)}\right]:\frac{x^2+1}{\left(x-6\right)\left(x+6\right)}=\)
\(=\left[\frac{6x^2+37x+6+6x^2-37x+6}{x\left(x-6\right)\left(x+6\right)}\right].\frac{\left(x-6\right)\left(x+6\right)}{x^2+1}=\)
\(=\frac{12\left(x^2+1\right)}{x\left(x-6\right)\left(x+6\right)}.\frac{\left(x-6\right)\left(x+6\right)}{x^2+1}=\frac{12}{x}\left(dpcm\right)\)