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1.a)\(\frac{x^3}{x^2-4}-\frac{x}{x-2}-\frac{2}{x+2}\)
\(=\frac{x^3}{\left(x+2\right)\left(x-2\right)}-\frac{x}{x-2}-\frac{2}{x+2}\)
Để biểu thức được xác định thì:\(\left(x+2\right)\left(x-2\right)\ne0\)\(\Rightarrow x\ne\pm2\)
\(\left(x+2\right)\ne0\Rightarrow x\ne-2\)
\(\left(x-2\right)\ne0\Rightarrow x\ne2\)
Vậy để biểu thức xác định thì : \(x\ne\pm2\)
b) để C=0 thì ....
1, c , bn Nguyễn Hữu Triết chưa lm xong
ta có : \(/x-5/=2\)
\(\Rightarrow\orbr{\begin{cases}x-5=2\\x-5=-2\end{cases}}\Rightarrow\orbr{\begin{cases}x=7\\x=3\end{cases}}\)
thay x = 7 vào biểu thứcC
\(\Rightarrow C=\frac{4.7^2\left(2-7\right)}{\left(7-3\right)\left(2+7\right)}=\frac{-988}{36}=\frac{-247}{9}\)KL :>...
thay x = 3 vào C
\(\Rightarrow C=\frac{4.3^2\left(2-3\right)}{\left(3-3\right)\left(3+7\right)}\)
=> ko tìm đc giá trị C tại x = 3
a,ĐK: \(\hept{\begin{cases}x\ne0\\x\ne\pm3\end{cases}}\)
b, \(A=\left(\frac{9}{x\left(x-3\right)\left(x+3\right)}+\frac{1}{x+3}\right):\left(\frac{x-3}{x\left(x+3\right)}-\frac{x}{3\left(x+3\right)}\right)\)
\(=\frac{9+x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}:\frac{3\left(x-3\right)-x^2}{3x\left(x+3\right)}\)
\(=\frac{x^2-3x+9}{x\left(x-3\right)\left(x+3\right)}.\frac{3x\left(x+3\right)}{-x^2+3x-9}=\frac{-3}{x-3}\)
c, Với x = 4 thỏa mãn ĐKXĐ thì
\(A=\frac{-3}{4-3}=-3\)
d, \(A\in Z\Rightarrow-3⋮\left(x-3\right)\)
\(\Rightarrow x-3\inƯ\left(-3\right)=\left\{-3;-1;1;3\right\}\Rightarrow x\in\left\{0;2;4;6\right\}\)
Mà \(x\ne0\Rightarrow x\in\left\{2;4;6\right\}\)
a: \(A=\left(\dfrac{x}{x^2-4}+\dfrac{4}{x-2}+\dfrac{1}{x+2}\right):\dfrac{3x+3}{x^2+2x}\)
\(=\dfrac{x+4x+8+x-2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x\left(x+2\right)}{3\left(x+1\right)}\)
\(=\dfrac{6\left(x+1\right)\cdot x\left(x+2\right)}{3\left(x+1\right)\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{2x}{x-2}\)
a, A xác định
\(\Leftrightarrow3x^3-19x^2+33x-9\ne0\)
\(\Leftrightarrow3x^3-x^2-18x^2+6x+27x-9\ne0\)
\(\Leftrightarrow x^2\left(3x-1\right)-6x\left(3x-1\right)+9\left(3x-1\right)\ne0\)
\(\Leftrightarrow\left(3x-1\right)\left(x-3\right)^2\ne0\Leftrightarrow\hept{\begin{cases}x\ne\frac{1}{3}\\x\ne3\end{cases}}\)
b, \(\frac{3x^3-14x^2+3x+36}{3x^2-19x^2+33x-9}=\frac{3x^2\left(x-3\right)-5x\left(x-3\right)-12\left(x-3\right)}{\left(3x-1\right)\left(x-3\right)^2}\)
\(=\frac{\left(3x^2-5x-12\right)\left(x-3\right)}{\left(3x-1\right)\left(x-3\right)^2}=\frac{\left(3x+4\right)\left(x-3\right)^2}{\left(3x-1\right)\left(x-3\right)^2}=\frac{3x+4}{3x-1}\)
\(A=0\Leftrightarrow\frac{3x+4}{3x-1}=0\Leftrightarrow3x+4=0\Leftrightarrow x=-\frac{4}{3}\) (thỏa mãn ĐKXĐ)
c, \(A=\frac{3x+4}{3x-1}=1+\frac{5}{3x-1}\in Z\Rightarrow5⋮\left(3x-1\right)\)
\(\Rightarrow3x-1\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\)
\(\Rightarrow x\in\left\{-\frac{4}{3};0;\frac{2}{3};2\right\}\)
Mà \(x\in Z,x\ne\left\{\frac{1}{3};3\right\}\Rightarrow x\in\left\{0;2\right\}\)
Bài của Hùng rất thông minh
Đang định có cách khác mà dài hơn cách Hùng nên thui
^^ 2k5 kết bạn nhé
để A xác định
\(\Rightarrow\hept{\begin{cases}x+2\ne0\\x-2\ne0\\x^2\ne4\end{cases}}\Rightarrow x\ne\pm2\)
\(A=\frac{4}{x+2}+\frac{3}{x-2}-\frac{5x-6}{x^2-4}\)
\(A=\frac{4.x-8}{\left(x+2\right).\left(x-2\right)}+\frac{3.x+6}{\left(x-2\right).\left(x+2\right)}-\frac{5x-6}{\left(x-2\right).\left(x+2\right)}\)
\(A=\frac{4x-8+3x+6-5x+6}{\left(x+2\right).\left(x-2\right)}=\frac{2.\left(x+2\right)}{\left(x+2\right).\left(x-2\right)}=\frac{2}{x-2}\)
\(\frac{4}{x+2}+\frac{3}{x-2}-\frac{5x-6}{x^2-4}=\frac{4}{x+2}+\frac{3}{x-2}-\frac{5x-6}{\left(x+2\right)\left(x-2\right)}\)
\(=\frac{4x-8}{\left(x+2\right)\left(x-2\right)}+\frac{3x+4}{\left(x-2\right)\left(x+2\right)}-\frac{5x-6}{\left(x-2\right)\left(x+2\right)}=\frac{4x-8+3x+4-5x+6}{\left(x+2\right)\left(x-2\right)}\)
\(=\frac{2x+2}{\left(x+2\right)\left(x-2\right)}=\frac{2x+2}{x^2-4}\)
C, \(x=4\Rightarrow A=\frac{2x+2}{x^2-4}=\frac{-6}{12}=\frac{-1}{2}\)
d, \(A\inℤ\Leftrightarrow2x+2⋮x^2-4\Leftrightarrow2x^2+2x-2x^2+8⋮x^2-4\Leftrightarrow2x+8⋮x^2-4\)
\(\Leftrightarrow2x^2+8x⋮x^2-4\Leftrightarrow16⋮x^2-4\)
\(x^2-4\inℕ\)
\(\Rightarrow x^2\in\left\{0;4;12\right\}\)
Thử lại thì 12 ko là số chính phương vậy x=0 hoặc x=2 thỏa mãn
mk học lớp 6 mong mn thông cảm nếu có sai sót
a) ĐKXĐ: \(x\notin\left\{3;-3;-2\right\}\)
Ta có: \(P=\left(\dfrac{2x-1}{x+3}-\dfrac{x}{3-x}-\dfrac{3-10x}{x^2-9}\right):\dfrac{x+2}{x-3}\)
\(=\left(\dfrac{\left(2x-1\right)\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}+\dfrac{x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{3-10x}{\left(x-3\right)\left(x+3\right)}\right):\dfrac{x+2}{x-3}\)
\(=\dfrac{2x^2-6x-x+3+x^2+3x-3+10x}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+2}{x-3}\)
\(=\dfrac{3x^2+6x}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+2}{x-3}\)
\(=\dfrac{3x\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{x-3}{x+2}\)
\(=\dfrac{3x}{x+3}\)
b) Ta có: \(x^2-7x+12=0\)
\(\Leftrightarrow x^2-3x-4x+12=0\)
\(\Leftrightarrow x\left(x-3\right)-4\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(loại\right)\\x=4\left(nhận\right)\end{matrix}\right.\)
Thay x=4 vào biểu thức \(P=\dfrac{3x}{x+3}\), ta được:
\(P=\dfrac{3\cdot4}{4+3}=\dfrac{12}{7}\)
Vậy: Khi \(x^2-7x+12=0\) thì \(P=\dfrac{12}{7}\)
\(B=\frac{5}{x+3}+\frac{3}{x-3}-\frac{5x+3}{x^2-9}\)
\(B=\frac{5}{x+3}+\frac{3}{x-3}-\frac{5x+3}{\left(x-3\right)\left(x+3\right)}\)
B xác định \(\Leftrightarrow\hept{\begin{cases}x-3\ne0\\x+3\ne0\end{cases}\Leftrightarrow}x\ne\pm3\)
Vậy B xác định \(\Leftrightarrow x\ne\pm3\)
\(B=\frac{5}{x+3}+\frac{3}{x-3}-\frac{5x+3}{x^2-9}\)
\(B=\frac{5}{x+3}+\frac{3}{x-3}-\frac{5x+3}{\left(x-3\right)\left(x+3\right)}\)
\(B=\frac{5\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{3\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{5x+3}{\left(x-3\right)\left(x+3\right)}\)
\(B=\frac{5x-15+3x+9-5x-3}{\left(x+3\right)\left(x-3\right)}\)
\(B=\frac{3x-9}{\left(x+3\right)\left(x-3\right)}\)
\(B=\frac{3\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}\)
\(B=\frac{3}{x+3}\)
mk cần gấp lắm các bạn ạk
BÀI 1:
a) \(ĐKXĐ:\) \(x-3\)\(\ne\)\(0\)
\(\Leftrightarrow\)\(x\)\(\ne\)\(3\)
b) \(A=\frac{x^3-3x^2+4x-1}{x-3}\)
\(=\frac{\left(x^3-3x^2\right)+\left(4x-12\right)+11}{x-3}\)
\(=\frac{x^2\left(x-3\right)+4\left(x-3\right)+11}{x-3}\)
\(=x^2+4+\frac{11}{x-3}\)
Để \(A\)có giá trị nguyên thì \(\frac{11}{x-3}\)có giá trị nguyên
hay \(x-3\)\(\notinƯ\left(11\right)=\left\{\pm1;\pm11\right\}\)
Ta lập bảng sau
\(x-3\) \(-11\) \(-1\) \(1\) \(11\)
\(x\) \(-8\) \(2\) \(4\) \(14\)
Vậy....