Cho A\(\frac{x^2-2x}{x^2-4x+4}\)(x\(\ne\)2)
a,Rút gọn A
b, Tìm x\(\in\)Z để A\(\in\)Z
1) Cho
\(A=\frac{4.x-1}{x-2}-\frac{x-3}{x-1}+\frac{-2x+4}{x^2-3.x+2}\)
a) Rút gọn A
b) Tìm \(x\in Z\) để \(A\in Z\)
a) \(A=\frac{4x-1}{x-2}-\frac{x-3}{x-1}+\frac{-2x+4}{x^2-3x+2}\)
\(\Leftrightarrow A=\frac{4x-1}{x-2}-\frac{x-3}{x-1}+\frac{-2x+4}{x^2-x-2x+2}\)
\(\Leftrightarrow A=\frac{4x-1}{x-2}-\frac{x-3}{x-1}+\frac{-2x+4}{x\left(x-1\right)-2\left(x-1\right)}\)
\(\Leftrightarrow A=\frac{4x-1}{x-2}-\frac{x-3}{x-1}+\frac{-2x+4}{\left(x-1\right)\left(x-2\right)}\)
\(\Leftrightarrow A=\frac{\left(4x-1\right)\left(x-1\right)-\left(x-3\right)\left(x-2\right)-2x+4}{\left(x-2\right)\left(x-1\right)}\)
\(\Leftrightarrow A=\frac{4x^2-4x-x+1-x^2+2x+3x-6-2x+4}{\left(x-2\right)\left(x-1\right)}\)
\(\Leftrightarrow A=\frac{3x^2-2x-1}{\left(x-2\right)\left(x-1\right)}\)
\(\Leftrightarrow A=\frac{3x^2-3x+\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}\)\(=\frac{3x\left(x-1\right)+\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}\)\(=\frac{\left(x-1\right)\left(3x+1\right)}{\left(x-2\right)\left(x-1\right)}\)\(=\frac{3x+1}{x-2}\)
b)\(\frac{3x+1}{x-2}=\frac{3x-6+7}{x-2}=\frac{3x-6}{x-2}+\frac{7}{x-2}=3+\frac{7}{x-2}\)
Ta có : \(x-2\inƯ_7\left\{-7;-1;1;7\right\}\)
\(\Rightarrow\left[\begin{array}{nghiempt}x-2=-7\\x-2=-1\\x-2=1\\x-2=7\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}\text{x=-5}\\\text{x=1}\\\text{x=3}\\\text{x}=9\end{array}\right.\)
\(\text{x}=1\) (loại)
Vậy giá trị nguyên tập hợp x là:
x=-5;3;9
Cho A = \(\left(\frac{2x-3}{4x^2-12x+5}+\frac{3x-8}{13x-2x^2-20}-\frac{3}{2x-1}\right):\frac{21+2x-2x^2}{4x^2+4x-3}+1\)
a, Rút gọn .
b, Tìm \(x\in Z\)để \(A\in Z\).
c, Tìm x để \(A\ge0\)
a. ĐKXĐ : \(x\ne\frac{1}{2};\frac{5}{2};4;-\frac{3}{2};\frac{1\pm\sqrt{43}}{2}\)
\(A=\left(\frac{2x-3}{4x^2-12x+5}+\frac{3x-8}{13x-2x^2-20}-\frac{3}{2x-1}\right):\frac{21+2x-2x^2}{4x^2+4x-3}+\)
\(=\left(\frac{2x-3}{\left(2x-1\right)\left(2x-5\right)}-\frac{3x-8}{\left(2x-5\right)\left(x-4\right)}-\frac{3}{2x-1}\right).\frac{\left(2x-1\right)\left(2x+3\right)}{21+2x-2x^2}+1\)
\(=\frac{\left(2x-3\right)\left(x-4\right)-\left(3x-8\right)\left(2x-1\right)-3\left(2x-5\right)\left(x-4\right)}{\left(2x-1\right)\left(2x-5\right)\left(x-4\right)}.\frac{\left(2x-1\right)\left(2x+3\right)}{21+2x-2x^2}+1\)
\(=\frac{-10x^2+47x-56}{\left(2x-5\right)\left(x-4\right)}.\frac{2x+3}{-2x^2+2x+21}+1\) số to wa
cho biểu thức :
A = \(\left(\frac{x}{x^2-4}+\frac{1}{x+2}-\frac{2}{x-2}\right):\left(1-\frac{x}{x+2}\right)\) (với \(x\ne+-2\))
a/ Rút gọn A
b/ Tính giá trị của A khi x = - 4
c/ Tìm \(x\in Z\) để \(A\in Z\)
a, \(A=\left(\frac{x}{x^2-4}+\frac{1}{x+2}-\frac{2}{x-2}\right):\left(1-\frac{x}{x+2}\right)\)
\(=\left(\frac{x}{\left(x-2\right)\left(x+2\right)}+\frac{1}{x+2}-\frac{2}{x-2}\right):\left(1-\frac{x}{x+2}\right)\)
=\(\left(\frac{x+x-2-2x-4}{\left(x-2\right)\left(x+2\right)}\right):\left(\frac{x+2-x}{x+2}\right)\)
\(=\frac{-6}{\left(x-2\right)\left(x+2\right)}.\frac{x+2}{2}\)
\(=\frac{-3}{x-2}\)
b. Thay : x=-4
=>-3/x-2=-3/(-4)-2=1/2
câu a quy đồng mẫu lên: x^2-4=(x+2)(x-2). câu b thì thay vào. câu c toán 7 tự làm
Câu 1 : Thực hiện phép tính
a) \(\frac{3}{x+3}-\frac{x-6}{x^2+3x}\)
b) \(\frac{2x^2-x}{x-1}+\frac{x+1}{1-x}+\frac{2-x^2}{x-1}\)
Câu 2 : Cho biểu thức A= \(\left(\frac{x}{x^2-4}+\frac{1}{x+2}-\frac{2}{x-2}\right):\left(1-\frac{x}{x+2}\right)\left(Vớix\ne\pm2\right)\)
a) Rút gọn A
b) tính giá trị A khi x = -4
c) tìm \(x\in Z\)để \(A\in Z\)
Câu 1 :
a, \(\frac{3}{x+3}-\frac{x-6}{x^2+3x}=\frac{3x-x+6}{x\left(x+3\right)}=\frac{2x+6}{x\left(x+3\right)}=\frac{2}{x}\)
b, \(\frac{2x^2-x}{x-1}+\frac{x+1}{1-x}+\frac{2-x^2}{x-1}=\frac{2x^2-x-x-1+2-x^2}{x-1}\)
\(=\frac{x^2-2x+1}{x-1}=\frac{\left(x-1\right)^2}{x-1}=x-1\)
Bài 2 :
a, Với \(x\ne\pm2\)
\(A=\left(\frac{x}{x^2-4}+\frac{1}{x+2}-\frac{2}{x-2}\right):\left(1-\frac{x}{x+2}\right)\)
\(=\left(\frac{x+x-2-2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\right):\left(\frac{x+2-x}{x+2}\right)\)
\(=\frac{-6}{\left(x-2\right)\left(x+2\right)}.\frac{x+2}{2}=\frac{-3}{x-2}\)
b, Thay x = -4 vào biểu thức trên ta được :
\(-\frac{3}{-4-2}=-\frac{3}{-6}=\frac{1}{2}\)
c, Để A \(\inℤ\Rightarrow x-2\inƯ\left(-3\right)=\left\{\pm1;\pm3\right\}\)
x - 2 | 1 | -1 | 3 | -3 |
x | 3 | 1 | 5 | -1 |
Cho phân thức: F(x)=$\frac{x^4+x^3-x^2-2x-2}{x^4+2x^3-x^2-4x-2}$x4+x3−x2−2x−2x4+2x3−x2−4x−2 (x$\in Z$∈Z)
a/ Rút gọn phân thức
b/Xác định giá trị của x để phân thức có giá trị nhỏ nhất
A=\(\left(\frac{x^3}{x^{3^{ }}-4x}+\frac{6}{6-3x}+\frac{1}{2+x}\right):\left(x+2+\frac{10-x^2}{x-2}\right)\)
a. Rút gọn A
b. Tìm x\(\in\)Z để A\(\in\)Z
c. Tìm x biết \(|B|\)>1
A=\(\frac{x-5}{x+2\sqrt{x}-3}+\frac{1}{\sqrt{x}+3}+\frac{2}{\sqrt{x}-1}\) (x\(\ge0\), x \(\ne\)1)
a) Rút gọn A
b) Tìm x để A\(\le\)\(\frac{1}{2}\)
c) Tìm x \(\in z\)để A \(\in z\)
Cho biểu thức:
A=x/2- (1/x-4x-2/1-2x) :(1+4x-x2 +1/x2 -2x)
a,rút gọn A
b,tìm x∈ Z để A∈Z
Cho C = \(\frac{3\sqrt{x}+2}{2\sqrt{x}-1}+\frac{\sqrt{x}-1}{\sqrt{x}+4}-\frac{x-6\sqrt{x}+5}{2x+7\sqrt{x}-4}.\)
a) rút gọn C
b) tìm x\(\in\)Z để C \(\in\)Z
c) tìm x để C > \(\frac{1}{2}\)