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a) \(\frac{3x}{2x+4}+\frac{x+3}{x^2-4}\)
\(=\frac{3x}{2\left(x+2\right)}+\frac{x+3}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{3x\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}+\frac{2\left(x+3\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{3x\left(x-2\right)+2\left(x+3\right)}{2\left(x+2\right)\left(x-2\right)}\)
\(=\frac{3x^2-6x+2x+6}{2\left(x^2-4\right)}\)
\(=\frac{3x^2-4x+6}{2\left(x^2-4\right)}\)
\(a,\left(x-2\right).\left(x-3\right)-\left(x+3\right).\left(x-3\right)\)
\(=\left(x-3\right).\left(x-2-x+3\right)=x-3\)
\(b,\frac{\left(x^2+4x+4\right)}{x+2}-4x+5=\frac{\left(x+2\right)^2}{x+2}-4x+5\)
\(x+2-4x+5=-3x+7\)
a) \(\left(x-2\right)\left(x-3\right)-\left(x+3\right)\left(x-3\right)\)
\(=\left(x^2-5x+6\right)-\left(x^2-9\right)\)
\(=x^2-5x+6-x^2+9\)
\(=15-5x\)
b) \(\left(x^2+4x+4\right):\left(x+2\right)-\left(4x-5\right)\)
\(=\left(x+2\right)^2:\left(x+2\right)-\left(4x-5\right)\)
\(=\left(x+2\right)-4x+5\)
\(=x+2-4x+5\)
\(=7-3x\)
Trả lời:
1) \(\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)=\left(\sqrt{x}\right)^2-2\sqrt{x}+\sqrt{x}-2=x-\sqrt{x}-2\)
2) \(\left(x+4\right)\left(x-2\right)-\left(x-3\right)^2=x^2-2x+4x-8-\left(x^2-6x+9\right)\)\(=x^2+2x-8-x^2+6x-9=8x-17\)
3) \(3x\left(2x^3-3x^2+5\right)=6x^4-9x^3+15x\)
\(\frac{4-x}{x^3+2x}-\frac{x+5}{x^3-x^2+2x-2}\)( ĐKXĐ : \(x\ne1\))
\(=\frac{4-x}{x\left(x^2+2\right)}-\frac{x+5}{x^2\left(x-1\right)+2\left(x-1\right)}\)
\(=\frac{4-x}{x\left(x^2+2\right)}-\frac{x+5}{\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{\left(4-x\right)\left(x-1\right)}{x\left(x-1\right)\left(x^2+2\right)}-\frac{x\left(x+5\right)}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-x^2+5x-4}{x\left(x-1\right)\left(x^2+2\right)}-\frac{x^2+5x}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-x^2+5x-4-\left(x^2+5x\right)}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-x^2+5x-4-x^2-5x}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-2x^2-4}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-2\left(x^2+2\right)}{x\left(x-1\right)\left(x^2+2\right)}\)
\(=\frac{-2}{x\left(x-1\right)}=\frac{-2}{x\left(x-1\right)}\)
Đang đánh máy thì bấm gửi -..-
a) \(\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}=\dfrac{15x.2y^2}{7y^3.x^2}=\dfrac{30}{7xy}\)
b) \(\dfrac{4y^2}{11x^4}.\left(-\dfrac{3x^2}{8y}\right)=\dfrac{-4y^2.3x^2}{11x^4.8y}=\dfrac{-3y}{22x^2}\)
c) \(\dfrac{x^3-8}{5x+20}.\dfrac{x^2+4x}{x^2+2x+4}\\ =\dfrac{\left(x-2\right)\left(x^2+2x+4\right)}{5\left(x+4\right)}.\dfrac{x\left(x+4\right)}{x^2+2x+4}\\ =\dfrac{x^2-2x}{5}\)
\(1.\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)
\(=\sqrt{x}\left(\sqrt{x}-2\right)+1\left(\sqrt{x}-2\right)\)
\(=x-2\sqrt{x}+\sqrt{x}-2\)
\(=x-\sqrt{x}-2\)
\(2.\left(x+4\right)\left(x-2\right)-\left(x-3\right)^2\)
\(=x\left(x-2\right)+4\left(x-2\right)-\left(x^2-6x+9\right)\)
\(=x^2-2x+4x-8-x^2+6x-9\)
\(=8x-17\)
a, 2x(1-3)=0
=>...................
hk tốt
a) \(2x^2-6x=0\)
\(2x\left(x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x=0\\x-3=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=3\end{cases}}\)
a) \(\dfrac{5x+10}{4x-8}.\dfrac{4-2x}{x+2}\\ =\dfrac{-5x-10}{8-4x}.\dfrac{4-2x}{x+2}\\ =\dfrac{-5\left(x+2\right)}{4\left(2-x\right)}.\dfrac{2\left(2-x\right)}{x+2}=\dfrac{-5}{2}\)
b)\(\dfrac{x^2-36}{2x+10}.\dfrac{3}{6-x}\\ =\dfrac{\left(x-6\right).\left(x+6\right)}{2\left(x+5\right)}.\dfrac{-3}{x-6}\\ =\dfrac{-3x-18}{2x+10}\)
a: \(=\dfrac{x^3-1}{x+2}\cdot\dfrac{x^2+x+1-x^2+1}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{x+2}{x+2}=1\)
b: \(=\dfrac{\left(x+2\right)\left(x-1\right)\left(x+1\right)}{2\left(x+5\right)}\cdot\left(\dfrac{x+1-2x+2}{\left(x-1\right)\left(x+1\right)}+\dfrac{1}{x+2}\right)\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)\left(x+1\right)}{2\left(x+5\right)}\cdot\left(\dfrac{-\left(x-3\right)}{\left(x-1\right)\left(x+1\right)}+\dfrac{1}{x+2}\right)\)
\(=\dfrac{\left(x+2\right)\left(x-1\right)\left(x+1\right)}{2\left(x+5\right)}\cdot\dfrac{-\left(x^2-x-6\right)+x^2-1}{\left(x-1\right)\left(x+1\right)\left(x+2\right)}\)
\(=\dfrac{-x^2+x+6+x^2-1}{2\left(x+5\right)}=\dfrac{x+5}{2\left(x+5\right)}=\dfrac{1}{2}\)
a) (x2 – 3x)(3x2 – x + 4)
= 3x4 - x3 + 4x2 - 9x3 + 3x2 -12x
= 3x4 - 10x3 + 7x2 - 12x