Chứng minh
\(\left(\frac{6}{x^2-6x}\right)\) + \(\frac{1}{x+6}\) ) . \(\frac{x^2+36}{x^2-36x}\) = 1
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TA
1
20 tháng 5 2017
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 \(\frac{1}{x}\)
DT
1
HN
17 tháng 2 2017
\(\left(\frac{x}{x^2-36}+\frac{6-x}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\)
đkxđ: \(x\ne0;x\ne\pm6\)
MTC=x(x+6)(x-6)
\(=\left[\frac{x}{\left(x+6\right)\left(x-6\right)}+\frac{6-x}{x\left(x+6\right)}\right]\cdot\frac{x\left(x+6\right)}{x\left(x-3\right)}-\frac{x}{x-6}\)
\(=\left[\frac{x^2}{x\left(x^2-36\right)}-\frac{\left(x-6\right)^2}{x\left(x^2-36\right)}\right]\cdot\frac{x\left(x+6\right)}{x\left(x-3\right)}-\frac{x}{x-6}\)
\(=\frac{12\left(x-3\right)}{x\left(x+6\right)\left(x-6\right)}\cdot\frac{x\left(x+6\right)}{x\left(x-3\right)}-\frac{x}{x-6}\)
\(=\frac{12}{x\left(x-6\right)}-\frac{x^2}{x\left(x-6\right)}\)
\(=\frac{12-x^2}{x\left(x-6\right)}\)
.....................
HY
10 tháng 2 2020
Xem lại đề gõ thiếu không? Ở \(\frac{2x-6}{x^2+6}\) phải là \(\frac{2x-6}{x^2+6x}\) chứ nhỉ
HY
10 tháng 2 2020
Sửa lại đề của bạn nhé
\(\left(\frac{x}{x^2-36}-\frac{x-6}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\\ =\left(\frac{x}{\left(x-6\right)\left(x+6\right)}-\frac{x-6}{x\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\left(\frac{x^2}{x\left(x-6\right)\left(x+6\right)}-\frac{\left(x-6\right)^2}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{\left(x-x+6\right)\left(x+x-6\right)}{x\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{6\left(2x-6\right)}{x\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{6x\left(2x-6\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)\left(2x-6\right)}+\frac{-x}{x-6}\\ =\frac{6}{x-6}+\frac{-x}{x-6}\\ =\frac{6-x}{x-6}\\ =-1\left(đpcm\right)\)
HN
18 tháng 12 2019
A = \(\left(\frac{x}{x^2-36}-\frac{x-6}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\)
= \(\left[\frac{x}{\left(x-6\right)\left(x+6\right)}-\frac{x-6}{x\left(x+6\right)}\right]:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)
= \(\left[\frac{x^2}{x\left(x-6\right)\left(x+6\right)}-\frac{\left(x-6\right)^2}{x\left(x-6\right)\left(x+6\right)}\right]:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)
= \(\frac{x^2-\left(x-6\right)^2}{x\left(x-6\right)\left(x+6\right)}:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)
= \(\frac{\left(x-x+6\right)\left(x+x-6\right)}{x\left(x-6\right)\left(x+6\right)}:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)
=
HN
18 tháng 12 2019
= \(\frac{x\left(2x-6\right)}{x\left(x-6\right)\left(x+6\right)}:\frac{2x-6}{x\left(x+6\right)}-\frac{x}{x-6}\)
= \(\frac{2x-6}{\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}\) \(-\frac{x}{x-6}\)
= \(\frac{x}{x-6}-\frac{x}{x-6}\)
= 0
công trừ nhân phia phân thwscc đi