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\(\left(\frac{x}{x^2-36}+\frac{6-x}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\)
đkxđ: \(x\ne0;x\ne\pm6\)
MTC=x(x+6)(x-6)
\(=\left[\frac{x}{\left(x+6\right)\left(x-6\right)}+\frac{6-x}{x\left(x+6\right)}\right]\cdot\frac{x\left(x+6\right)}{x\left(x-3\right)}-\frac{x}{x-6}\)
\(=\left[\frac{x^2}{x\left(x^2-36\right)}-\frac{\left(x-6\right)^2}{x\left(x^2-36\right)}\right]\cdot\frac{x\left(x+6\right)}{x\left(x-3\right)}-\frac{x}{x-6}\)
\(=\frac{12\left(x-3\right)}{x\left(x+6\right)\left(x-6\right)}\cdot\frac{x\left(x+6\right)}{x\left(x-3\right)}-\frac{x}{x-6}\)
\(=\frac{12}{x\left(x-6\right)}-\frac{x^2}{x\left(x-6\right)}\)
\(=\frac{12-x^2}{x\left(x-6\right)}\)
.....................
A = \(\left(\frac{x}{x^2-36}-\frac{x-6}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\)
= \(\left[\frac{x}{\left(x-6\right)\left(x+6\right)}-\frac{x-6}{x\left(x+6\right)}\right]:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)
= \(\left[\frac{x^2}{x\left(x-6\right)\left(x+6\right)}-\frac{\left(x-6\right)^2}{x\left(x-6\right)\left(x+6\right)}\right]:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)
= \(\frac{x^2-\left(x-6\right)^2}{x\left(x-6\right)\left(x+6\right)}:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)
= \(\frac{\left(x-x+6\right)\left(x+x-6\right)}{x\left(x-6\right)\left(x+6\right)}:\frac{2\left(x-3\right)}{x\left(x+6\right)}-\frac{x}{x-6}\)
=
= \(\frac{x\left(2x-6\right)}{x\left(x-6\right)\left(x+6\right)}:\frac{2x-6}{x\left(x+6\right)}-\frac{x}{x-6}\)
= \(\frac{2x-6}{\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}\) \(-\frac{x}{x-6}\)
= \(\frac{x}{x-6}-\frac{x}{x-6}\)
= 0
= ( x/(x-6)(x+6) - x-6/x(x+6) ) : 2x-6/x2 + 6x + 6/6-x
=( x2/x(x+6)(x-6) - (x -6 )(x-6)/x(x+6)(x-6) ) : .....
= (12x -36 / x(x+6)(x-6) : 2x-6/ x2 + 6x )+ 6/6-x
=6/x-6 + 6/6-x
= 6-6/ x-6
=0/x-6
câu trước mình thiếu 6/6-x
Xem lại đề gõ thiếu không? Ở \(\frac{2x-6}{x^2+6}\) phải là \(\frac{2x-6}{x^2+6x}\) chứ nhỉ
Sửa lại đề của bạn nhé
\(\left(\frac{x}{x^2-36}-\frac{x-6}{x^2+6x}\right):\frac{2x-6}{x^2+6x}+\frac{x}{6-x}\\ =\left(\frac{x}{\left(x-6\right)\left(x+6\right)}-\frac{x-6}{x\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\left(\frac{x^2}{x\left(x-6\right)\left(x+6\right)}-\frac{\left(x-6\right)^2}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{\left(x-x+6\right)\left(x+x-6\right)}{x\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{6\left(2x-6\right)}{x\left(x-6\right)\left(x+6\right)}.\frac{x\left(x+6\right)}{2x-6}+\frac{-x}{x-6}\\ =\frac{6x\left(2x-6\right)\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)\left(2x-6\right)}+\frac{-x}{x-6}\\ =\frac{6}{x-6}+\frac{-x}{x-6}\\ =\frac{6-x}{x-6}\\ =-1\left(đpcm\right)\)
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 \(\frac{1}{x}\)
\(\left( \frac{x}{x^2-36} - \frac{6}{x^2+6x} \right) : \frac{2x-6}{x^2+6x} + \frac{x}{6-x}\) (đkxđ: \(x \neq 0;\ x \neq \pm 6;\ x \neq 3\) )
\(= \left[ \frac{x}{(x-6)(x+6)} - \frac{6}{x(x+6)} \right] \cdot \frac{x(x+6)}{2(x-3)} - \frac{x}{x-6}\)
\(= \frac{x^2 - 6(x-6)}{x(x-6)(x+6)} \cdot \frac{x(x+6)}{2(x-3)} - \frac{x}{x-6}\)
\(= \frac{x^2 - 6x + 36}{x(x-6)(x+6)} \cdot \frac{x(x+6)}{2(x-3)} - \frac{x}{x-6}\)
\(= \frac{x^2 - 6x + 36}{2(x-6)(x-3)} - \frac{x}{x-6}\)
\(= \frac{x^2 - 6x + 36 - 2x(x-3)}{2(x-6)(x-3)}\)
\(= \frac{x^2 - 6x + 36 - 2x^2 + 6x}{2(x-6)(x-3)}\)
\(=\frac{-x^2 + 36}{2(x-6)(x-3)}=\frac{-(x^2 - 36)}{2(x-6)(x-3)}\)
\(=\frac{-(x-6)(x+6)}{2(x-6)(x-3)}=\frac{-(x+6)}{2(x-3)}\)
Ta có biểu thức:
\(\left(\right. \frac{x}{x^{2} - 36} - \frac{6}{x^{2} + 6 x} \left.\right) : \frac{2 x - 6}{x^{2} + 6 x} + \frac{x}{6 - x}\)Điều kiện xác định
\(x \neq - 6 , \textrm{ }\textrm{ } x \neq 6 , \textrm{ }\textrm{ } x \neq 3.\)Bước 1. Rút gọn biểu thức trong ngoặc
Phân tích mẫu:
\(x^{2} - 36 = \left(\right. x - 6 \left.\right) \left(\right. x + 6 \left.\right) , x^{2} + 6 x = x \left(\right. x + 6 \left.\right) .\)Khi đó:
\(\frac{x}{\left(\right. x - 6 \left.\right) \left(\right. x + 6 \left.\right)} - \frac{6}{x \left(\right. x + 6 \left.\right)}\)Quy đồng mẫu số \(x \left(\right. x - 6 \left.\right) \left(\right. x + 6 \left.\right)\):
\(= \frac{x^{2} - 6 \left(\right. x - 6 \left.\right)}{x \left(\right. x - 6 \left.\right) \left(\right. x + 6 \left.\right)} = \frac{x^{2} - 6 x + 36}{x \left(\right. x - 6 \left.\right) \left(\right. x + 6 \left.\right)} .\)Bước 2. Thực hiện phép chia
\(: \frac{2 x - 6}{x \left(\right. x + 6 \left.\right)} = \times \frac{x \left(\right. x + 6 \left.\right)}{2 x - 6} .\)Rút gọn \(x \left(\right. x + 6 \left.\right)\):
\(= \frac{x^{2} - 6 x + 36}{\left(\right. x - 6 \left.\right) \left(\right. 2 x - 6 \left.\right)} .\)Vì
\(2 x - 6 = 2 \left(\right. x - 3 \left.\right) ,\)nên
\(= \frac{x^{2} - 6 x + 36}{2 \left(\right. x - 6 \left.\right) \left(\right. x - 3 \left.\right)} .\)Bước 3. Rút gọn hạng tử cuối
\(\frac{x}{6 - x} = - \frac{x}{x - 6} .\)Bước 4. Cộng hai phân thức
\(\frac{x^{2} - 6 x + 36}{2 \left(\right. x - 6 \left.\right) \left(\right. x - 3 \left.\right)} - \frac{x}{x - 6}\)Quy đồng mẫu \(2 \left(\right. x - 6 \left.\right) \left(\right. x - 3 \left.\right)\):
\(= \frac{x^{2} - 6 x + 36 - 2 x \left(\right. x - 3 \left.\right)}{2 \left(\right. x - 6 \left.\right) \left(\right. x - 3 \left.\right)} .\)Rút gọn tử:
\(x^{2} - 6 x + 36 - 2 x^{2} + 6 x = 36 - x^{2} .\)Do đó
\(= \frac{36 - x^{2}}{2 \left(\right. x - 6 \left.\right) \left(\right. x - 3 \left.\right)} = - \frac{\left(\right. x - 6 \left.\right) \left(\right. x + 6 \left.\right)}{2 \left(\right. x - 6 \left.\right) \left(\right. x - 3 \left.\right)} = - \frac{x + 6}{2 \left(\right. x - 3 \left.\right)} .\)Kết quả
\(\boxed{- \frac{x + 6}{2 \left(\right. x - 3 \left.\right)}}\)với điều kiện
\(\boxed{x \neq - 6 , \textrm{ }\textrm{ } x \neq 3 , \textrm{ }\textrm{ } x \neq 6.}\)tui ngửi dc mùi j đó bốc lên r