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a,(5x-2y)(x2-xy+1)=5x3-5x2+5x-2yx2+2xy2-2y
=5x3-7x2y+2xy2+5x-2y
b,(x-2)(x+2)(\(\dfrac{1}{2}\) x-5)=x2-4.\(\left(\dfrac{1}{2}x-5\right)\)
=\(\dfrac{1}{2}x^3-5x^2-2x+20\)
c,\(\left(x^2-2x+3\right)\left(\dfrac{1}{2}x-5\right)\)
=\(\dfrac{1}{2}x^3-5x^2-1x^2+10x+\dfrac{3}{2}x-15\)
=\(\dfrac{1}{2}x^3-6x^2+\dfrac{23}{2}x-15\)
d,\(\left(x^2-5\right)\left(x+3\right)+\left(x+4\right)\left(x-x^2\right)\)
=\(x^3+3x^2-5x-15+x^2-x^3+4x-4x^2\)
=\(-5x+4x-15\)
=\(-x-15\)
Chúc bạn học tốt(mỏi tay quá)
Câu 4:
a: ĐKXĐ: \(x\notin\left\{0;-5\right\}\)
b: \(A=\dfrac{x^2+2x}{2\left(x+5\right)}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x\left(x+5\right)}\)
\(=\dfrac{x^3+2x^2}{2x\left(x+5\right)}+\dfrac{2\left(x^2-25\right)}{2x\left(x+5\right)}+\dfrac{50-5x}{2x\left(x+5\right)}\)
\(=\dfrac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}\)
\(=\dfrac{x^3+4x^2-5x}{2x\left(x+5\right)}=\dfrac{x\left(x^2+4x-5\right)}{2x\left(x+5\right)}\)
\(=\dfrac{x\left(x+5\right)\left(x-1\right)}{2x\left(x+5\right)}=\dfrac{x-1}{2}\)
c: Để A=-3 thì x-1=-6
hay x=-5(loại)
Điều kiện:
\(x-1\ne0\Rightarrow x\ne1\)
\(x^3+x\ne0\Leftrightarrow x\ne0\)
\(M=\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(M=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\)
\(M=\left[x\left(x+5\right)+2\left(x+5\right)\right]\left[x\left(x+4\right)+3\left(x+4\right)\right]-24\)
\(M=\left(x^2+5x+2x+10\right)\left(x^2+4x+3x+12\right)-24\)
\(M=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
\(M=\left(x^2+7x+11-1\right)\left(x^2+7x+11+1\right)-24\)
\(M=\left(x^2+7x+11\right)^2-1-24\)
\(M=\left(x^2+7x+11\right)^2-25\)
\(M=\left(x^2+7x+11+5\right)\left(x^2+7x+11-5\right)\)
\(M=\left(x^2+7x+16\right)\left(x^2+7x+6\right)\)
Bài 1 : \(2\left(3x-1\right)-3x=10\)
\(\Leftrightarrow6x-2-3x=10\)
\(\Leftrightarrow3x=12\)
\(\Leftrightarrow x=4\)
Vậy...................
b ) \(\dfrac{x+1}{x}+1=\dfrac{3x-1}{x+1}+\dfrac{1}{x\left(x+1\right)}\left(1\right)\)
ĐKXĐ : \(x\ne0;x\ne-1\)
\(\left(1\right)\Rightarrow\left(x+1\right)^2+x\left(x+1\right)=x\left(3x-1\right)+1\)
\(\Leftrightarrow x^2+2x+1+x^2+x-3x^2+x-1=0\)
\(\Leftrightarrow-x^2+4x=0\)
\(\Leftrightarrow x\left(-x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(KTMĐKXĐ\right)\\x=4\left(TMĐKXĐ\right)\end{matrix}\right.\)
Vậy .......................
c ) \(\dfrac{2x+1}{3}-\dfrac{3x-2}{2}>\dfrac{1}{6}\)
\(\Leftrightarrow2\left(2x+1\right)-3\left(3x-2\right)>1\)
\(\Leftrightarrow4x+2-9x+6>1\)
\(\Leftrightarrow-5x>-7\)
\(\Leftrightarrow x< \dfrac{7}{5}.\)
Vậy .......
a ) \(A=\left(\dfrac{x^2-3}{x^2-9}+\dfrac{1}{x-3}\right):\dfrac{x}{x+3}.ĐKXĐ:x\ne3;x\ne-3\)
\(A=\left(\dfrac{x^2-3}{\left(x-3\right)\left(x+3\right)}+\dfrac{1}{\left(x-3\right)}\right).\dfrac{x+3}{x}\)
\(A=\dfrac{x^2-3x+x^2+3x}{x\left(x-3\right)\left(x+3\right)}.\dfrac{x+3}{x}\)
\(A=\dfrac{x+1}{x-3}\)
b ) \(\left|A\right|=3.\) thì x là ?
\(\left|\dfrac{x+1}{x-3}\right|=3\)
Kẻ bảng ra làm nha :D