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\(1,\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}=\frac{3}{2x+6}-\frac{x-6}{x\left(2x-6\right)}=\frac{3x-x+6}{x\left(2x-6\right)}=\frac{2x+6}{x\left(2x-6\right)}\)
\(2,\frac{1}{1-x}+\frac{2x}{x^2-1}=\frac{-1\left(x+1\right)+2x}{x^2-1}=\frac{x-1}{x^2-1}=\frac{1}{x+1}\)
\(3,\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{1}{x\left(y-x\right)}-\frac{1}{y\left(y-x\right)}=\frac{y-x}{xy\left(y-x\right)}=\frac{1}{xy}\)
\(4,\frac{5x+10}{4x-8}.\frac{4-2x}{x+2}=\frac{5\left(x+2\right)}{4\left(x-2\right)}.\frac{2\left(2-x\right)}{x+2}=\frac{-5}{2}\)
\(5,\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}=\frac{\left(1-2x\right)\left(1+2x\right)}{x\left(x+4\right)}.\frac{3x}{2\left(1-2x\right)}=\frac{3\left(1+2x\right)}{2x\left(x+4\right)}\)
\(6,\frac{12x}{5y^3}.\frac{15y^4}{8x^3}=\frac{9y}{2x^2}\)
Bài làm
a) \(\frac{4x-5}{8xy}+\frac{5-y}{8xy}=\frac{4x-5+5-y}{8xy}=\frac{4x-y}{8xy}\)
b) \(\frac{4x^2}{x-2}+\frac{3}{x-2}+\frac{19}{2-x}=\frac{4x^2}{x-2}+\frac{3}{x-2}-\frac{19}{x-2}=\frac{4x^2+3-19}{x-2}=\frac{4x^2-16}{x-2}=\frac{2\left(x-2\right)\left(2x+4\right)}{x-2}=2\left(2x+4\right)\)
c) \(\frac{2x^3+5}{x^2-x+1}-\frac{x^3+4}{x^2-x+1}=\frac{2x^3+5-x^3-4}{x^2-x+1}=\frac{2x^2-x^3+1}{x^2-x+1}\)
d) \(\frac{6}{5x-20}-\frac{x-5}{x^2-8x+16}=\frac{6}{5\left(x-4\right)}-\frac{x-5}{\left(x-4\right)^2}=\frac{6\left(x-4\right)}{5\left(x-4\right)^2}-\frac{\left(x-5\right)5}{5\left(x-4\right)^2}=\frac{6x-4-5x+25}{5\left(x-4\right)^2}=\frac{x+21}{5\left(x-4\right)^2}\)
# Học tốt #
b/ \(3-100x+8x^2=8x^2+x-300\)
\(\Leftrightarrow-101x=-303\)
\(\Rightarrow x=3\)
c/ \(5\left(5x+2\right)-10\left(8x-1\right)=6\left(4x+2\right)-150\)
\(\Leftrightarrow25x+10-80x+10=24x+12-150\)
\(\Leftrightarrow-79x=-158\)
\(\Rightarrow x=2\)
d/ \(3\left(3x+2\right)-\left(3x+1\right)=12x+10\)
\(\Leftrightarrow9x+6-3x-1=12x+10\)
\(\Leftrightarrow-6x=5\)
\(\Rightarrow x=-\frac{5}{6}\)
e/ \(30x-6\left(2x-5\right)+5\left(x+8\right)=210+10\left(x-1\right)\)
\(\Leftrightarrow30x-12x+30+5x+40=210+10x-10\)
\(\Leftrightarrow13x=130\)
\(\Rightarrow x=10\)
\(A=x^2-4x+1=\left(x-2\right)^2-3\ge-3\)
\(\Rightarrow A_{min}=-3\) khi \(x=2\)
\(B=4x^2+4x+11=\left(2x+1\right)^2+10\ge10\)
\(\Rightarrow B_{min}=10\) khi \(x=-\frac{1}{2}\)
\(C=\left(x-1\right)\left(x+6\right)\left(x+2\right)\left(x+3\right)=\left(x^2+5x-6\right)\left(x^2+5x+6\right)\)
\(=\left(x^2+5x\right)^2-36\ge-36\)
\(\Rightarrow C_{min}=-36\) khi \(\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)
\(D=-x^2-8x-16+21=21-\left(x+4\right)^2\le21\)
\(\Rightarrow C_{max}=21\) khi \(x=-4\)
\(E=-x^2+4x-4+5=5-\left(x-2\right)^2\le5\)
\(\Rightarrow E_{max}=5\) khi \(x=2\)
1,\(\frac{3}{2x+6}-\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x}{x\left(2x+6\right)}+\frac{x-6}{x\left(2x+6\right)}\)
=\(\frac{3x+x-6}{x\left(2x+6\right)}\)=\(\frac{4x-6}{x\left(2x+6\right)}=\frac{2\left(2x-3\right)}{x\left(2x+6\right)}\)
\(\frac{3}{x+1}-\frac{2}{x+3}=\frac{4x+5}{x^2+4x+3}\)
\(\Leftrightarrow\frac{3}{x+1}-\frac{2}{x+3}=\frac{4x+5}{\left(x+1\right)\left(x+3\right)}\)
\(\Leftrightarrow3\left(x+3\right)-2\left(x+1\right)=4x+5\)
\(\Leftrightarrow x+7=4x+5\)
\(\Leftrightarrow7=4x+5-x\)
\(\Leftrightarrow7=3x+5\)
\(\Leftrightarrow7-5=3x\)
\(\Leftrightarrow2=3x\)
\(\Leftrightarrow\frac{2}{3}=x\)
\(\Rightarrow x=\frac{2}{3}\)