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11)\(\dfrac{3x+1}{x-5}+\dfrac{2x}{x-5}=\dfrac{3x+2x+1}{x-5}=\dfrac{5x+1}{x-5}\)
12)\(\dfrac{4-x^2}{x-3}+\dfrac{2}{x^2-9}=\dfrac{4-x^2}{x-3}+\dfrac{2}{\left(x-3\right)\left(x+3\right)}=\dfrac{\left(4-x^2\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{2}{\left(x-3\right)\left(x+3\right)}=\dfrac{2+\left(2-x\right)\left(2+x\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)
13)
\(\dfrac{3}{4x-2}+\dfrac{2x}{4x^2-1}=\dfrac{3}{2\left(2x-1\right)}+\dfrac{2x}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{3\left(2x+1\right)}{2\left(2x-1\right)\left(2x+1\right)}+\dfrac{2.2x}{2\left(2x-1\right)\left(2x+1\right)}=\dfrac{6x+3+4x}{2\left(2x-1\right)\left(2x+1\right)}=\dfrac{10x+3}{2\left(2x-1\right)\left(2x+1\right)}\)
14)
\(\dfrac{2x+1}{2x-4}+\dfrac{5}{x^2-4}=\dfrac{2x+1}{2\left(x-2\right)}+\dfrac{5}{\left(x-2\right)\left(x+2\right)}=\dfrac{\left(2x+1\right)\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\dfrac{5.2}{2\left(x-2\right)\left(x+2\right)}=\dfrac{2x^2+5x+12}{2\left(x-2\right)\left(x+2\right)}\)
Ta có:
\(C=\dfrac{2n-3}{n-2}=\dfrac{2n-4+1}{n-2}=2+\dfrac{1}{n-2}\)
\(C\in Z\Leftrightarrow\dfrac{1}{n-2}\in Z\Leftrightarrow n-2\inƯ\left(1\right)=\left\{-1;1\right\}\)
\(\Rightarrow...\)
b1:
AMF đồng dạng ABC
tỉ số : AM/AF = AB/AC
AM/MF = AB/BC
AF/FM = AC/CB
MFD đồng dạng CFD
tỉ số : MF/FD= FD/DC
FM/MD = DC/CF
FD/DM = DF/FC
AFB đồng dạng CFB
tỉ số : AB/ BF = BF/FC
AF/AB =BF/ BC
AF / FB = CF/BC
Do 103 là số nguyên tố lẻ và 32y chẵn nên \(5x^2\) lẻ
Do đó \(x^2\) lẻ
\(\Leftrightarrow x^2:4\) dư 1
Mà \(32y⋮4\Leftrightarrow5x^2-32y:4\) dư 1
Mà \(103:4\) dư 3 nên PT vô nghiệm
Cau 2:
\(a,=\left(x^2-4\right)\left(x+1\right)=\left(x-2\right)\left(x+2\right)\left(x+1\right)\\ b,=\left(x-2\right)^2-y^2=\left(x-y-2\right)\left(x+y-2\right)\\ c,=\left(x^2+6x+9\right)\left(x^2-6x+9\right)=\left(x-3\right)^2\left(x+3\right)^2\\ d,=25-\left(x-y\right)^2=\left(25-x+y\right)\left(25+x-y\right)\\ e,=x^3-x^2-3x^2+3x+x-1=\left(x-1\right)\left(x^2-3x+1\right)\\ f,=3\left(x-y\right)-\left(x-y\right)^2=\left(3-x+y\right)\left(x-y\right)\)
Cau 3:
\(a,\Rightarrow\left(x-3\right)\left(2x+5\right)=0\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{5}{2}\end{matrix}\right.\\ b,\Rightarrow\left(x-2\right)\left(x+2-3+2x\right)=0\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{3}\end{matrix}\right.\\ c,\Rightarrow\left(2x+5-x-2\right)\left(2x+5+x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-3\\x=-\dfrac{7}{3}\end{matrix}\right.\\ d,\Rightarrow x^3-2x^2-2x+4=0\\ \Rightarrow\left(x-2\right)\left(x^2-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\\ e,\Rightarrow8x^3+4x^2-12x^2-6x+2x+1=0\\ \Rightarrow\left(2x+1\right)\left(4x^2-6x+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=\dfrac{3\pm\sqrt{5}}{4}\end{matrix}\right.\)
Thank bạn