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a: \(=5x^2-10x-5x^2+7x=-3x\)
b: \(=2x^3+3xy^2-4y-3xy^2=2x^3-4y\)
a) \(\dfrac{2\left(x-2\right)}{x\left(x-2\right)}=\dfrac{2}{x}\)
\(a,=\dfrac{2\left(x-2\right)}{x\left(x-2\right)}=\dfrac{2}{x}\\ b,=\dfrac{\left(1-3x\right)\left(2x-1\right)+2x\left(3x-2\right)-\left(3x-2\right)}{2x\left(2x-1\right)}\\ =\dfrac{\left(1-3x\right)\left(2x-1\right)+\left(2x-1\right)\left(3x-2\right)}{2x\left(2x-1\right)}\\ =\dfrac{\left(2x-1\right)\left(1-3x+3x-2\right)}{2x}=\dfrac{-1}{2x}\)
Lời giải:
$(2x-3)(x^2+1)=0$
\(\Leftrightarrow \left[\begin{matrix} 2x-3=0\\ x^2+1=0\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=\frac{3}{2}(\text{chọn})\\ x^2=-1<0(\text{vô lý})\end{matrix}\right.\)
Vậy pt có nghiệm $x=\frac{3}{2}$
\(\dfrac{2}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\\ \Leftrightarrow\dfrac{2.\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}-\dfrac{1.\left(x+1\right)}{\left(x+1\right)\left(x-2\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\\ \Leftrightarrow2x-4-x+1=3x-11\\ \Leftrightarrow x-3=3x-11\\ \Leftrightarrow x-3x=-11+3\\ \Leftrightarrow-2x=-8\\ \Leftrightarrow x=4\)
Vậy tập nghiệm của phương trình là S = { 4 }
ĐKXĐ:\(x\ne\pm1\)
\(\dfrac{x-1}{x+1}-\dfrac{x+1}{x-1}=\dfrac{14}{x^2-1}\\ \Leftrightarrow\dfrac{\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}-\dfrac{\left(x+1\right)^2}{\left(x+1\right)\left(x-1\right)}-\dfrac{14}{\left(x+1\right)\left(x-1\right)}=0\\ \Rightarrow x^2-2x+1-x^2-2x-1-14=0\\ \Leftrightarrow-4x-14=0\\ \Leftrightarrow x=-\dfrac{7}{2}\left(tm\right)\)
\(\Leftrightarrow3\left(2x-1\right)-2\left(3-x\right)=-1\)
=>6x-3-6+2x=-1
=>8x-9=-1
=>8x=8
hay x=1
\(\Leftrightarrow x\left(7-x\right)+\left(x+2\right)\left(x-4\right)=x+4\)
\(\Leftrightarrow7x-x^2+x^2-2x-8-x-4=0\)
=>4x-12=0
hay x=3(nhận)
ĐKXĐ:\(x\ne\pm4\)
\(\dfrac{x\left(7-x\right)}{x^2-16}+\dfrac{2+x}{x+4}=\dfrac{1}{x-4}\\ \Leftrightarrow\dfrac{x\left(7-x\right)}{\left(x-4\right)\left(x+4\right)}+\dfrac{\left(x-4\right)\left(2+x\right)}{\left(x-4\right)\left(x+4\right)}-\dfrac{x+4}{\left(x-4\right)\left(x+4\right)}=0\\ \Leftrightarrow\dfrac{7x-x^2+2x-8+x^2-4x-x-4}{\left(x-4\right)\left(x+4\right)}=0\\ \Rightarrow4x-12=0\\ \Leftrightarrow x=3\left(tm\right)\)
\(\Leftrightarrow2x\left(x+5\right)=3\left(x+5\right)\)
\(\Leftrightarrow2x\left(x+5\right)-3\left(x+5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(2x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=\dfrac{3}{2}\end{matrix}\right.\)
⇔2x(x+5)= 3(x+5)⇔ 2x(x+5)= 3(x+5)
⇔2x(x+5)−3(x+5)= 0⇔2x(x+5)−3(x+5)= 0
⇔(x+5)(2x−3)= 0⇔(x+5)(2x−3)= 0
⇔x= -5 hoặc x= 3/2.
\(ĐK:x\ne0;2\)
\(\Leftrightarrow\dfrac{x+2}{x}-\dfrac{2x+3}{2\left(x-2\right)}=0\)
\(\Leftrightarrow\dfrac{2\left(x-2\right)\left(x+2\right)-x\left(2x+3\right)}{2x\left(x-2\right)}=0\)
\(\Leftrightarrow2\left(x^2-4\right)-x\left(2x+3\right)=0\)
\(\Leftrightarrow2x^2-8-2x^2-3x=0\)
\(\Leftrightarrow-3x=8\Leftrightarrow x=-\dfrac{8}{3}\left(tm\right)\)
\(P=\dfrac{x}{2x-2}+\dfrac{x^2+1}{2-2x^2}\)
a: \(P=\dfrac{x}{2\left(x-1\right)}-\dfrac{x^2+1}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x^2+x-x^2-1}{2\left(x-1\right)\left(x+1\right)}=\dfrac{1}{2\left(x+1\right)}\)
b: Để P=-1/2 thì 1/2(x+1)=-1/2
=>x+1=-1
=>x=-2