Sửa đề: \(2x\left(3x-7\right)-\left(6x+5\right)\left(x-3\right)-2019=0\)

TA có: \(2x\left(3x-7\right)-\left(6x+5\right)\left(x-3\right)-2019=0\)

=>\(6x^2-14x-\left(6x^2-18x+5x-15\right)-2019=0\)

=>\(6x^2-14x-\left(6x^2-13x-15\right)-2019=0\)

=>\(6x^2-14x-6x^2+13x+15-2019=0\)

=>-x-2004=0

=>x+2004=0

=>x=-2004

a: \(\frac{x+1}{2x-6}-\frac{4}{2x-6}\)

\(=\frac{x+1-4}{2\left(x-3\right)}\)

\(=\frac{x-3}{2\left(x-3\right)}=\frac12\)

b: \(\frac{3x-4}{6x+3}-\frac{x-5}{6x+3}\)

\(=\frac{3x-4-x+5}{6x+3}\)

\(=\frac{2x+1}{3\left(2x+1\right)}=\frac13\)

c: \(\frac{x-1}{x-3}-\frac{3x-8}{3-x}+\frac{3-2x}{x-3}\)

\(=\frac{x-1}{x-3}+\frac{3x-8}{x-3}+\frac{3-2x}{x-3}\)

\(=\frac{x-1+3x-8+3-2x}{x-3}=\frac{2x-6}{x-3}=\frac{2\left(x-3\right)}{x-3}\)

=2

d: \(\frac{3}{x+5}-\frac{5}{x-7}\)

\(=\frac{3\left(x-7\right)-5\left(x+5\right)}{\left(x+5\right)\left(x-7\right)}=\frac{3x-21-5x-25}{\left(x+5\right)\left(x-7\right)}\)

\(=\frac{-2x-46}{\left(x+5\right)\left(x-7\right)}\)

e: \(\frac{3}{x+5}-\frac{5}{x-7}\)

\(=\frac{3\left(x-7\right)-5\left(x+5\right)}{\left(x+5\right)\left(x-7\right)}=\frac{3x-21-5x-25}{\left(x+5\right)\left(x-7\right)}\)

\(=\frac{-2x-46}{\left(x+5\right)\left(x-7\right)}\)

f: \(\frac{2}{x-2}+\frac{3}{x+2}+\frac{5x-18}{x^2-4}\)

\(=\frac{2}{x-2}+\frac{3}{x+2}+\frac{5x-18}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{2\left(x+2\right)+3\left(x-2\right)+5x-18}{\left(x-2\right)\left(x+2\right)}=\frac{2x+4+3x-6+5x-18}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{10x-20}{\left(x-2\right)\left(x+2\right)}=\frac{10}{x+2}\)

\(\Leftrightarrow2x^2-11x+5-2x^2+10x=25\Leftrightarrow-x=20\Leftrightarrow x=-20\)

b: =x-2

d: \(=-x^3+\dfrac{3}{2}-2x\)

* Trả lời:

\(\left(1\right)\) \(-3\left(1-2x\right)-4\left(1+3x\right)=-5x+5\)

\(\Leftrightarrow-3+6x-4-12x=-5x+5\)

\(\Leftrightarrow6x-12x+5x=3+4+5\)

\(\Leftrightarrow x=12\)

\(\left(2\right)\) \(3\left(2x-5\right)-6\left(1-4x\right)=-3x+7\)

\(\Leftrightarrow6x-15-6+24x=-3x+7\)

\(\Leftrightarrow6x+24x+3x=15+6+7\)

\(\Leftrightarrow33x=28\)

\(\Leftrightarrow x=\dfrac{28}{33}\)

\(\left(3\right)\) \(\left(1-3x\right)-2\left(3x-6\right)=-4x-5\)

\(\Leftrightarrow1-3x-6x+12=-4x-5\)

\(\Leftrightarrow-3x-6x+4x=-1-12-5\)

\(\Leftrightarrow-5x=-18\)

\(\Leftrightarrow x=\dfrac{18}{5}\)

\(\left(4\right)\) \(x\left(4x-3\right)-2x\left(2x-1\right)=5x-7\)

\(\Leftrightarrow4x^2-3x-4x^2+2x=5x-7\)

\(\Leftrightarrow-x-5x=-7\)

\(\Leftrightarrow-6x=-7\)

\(\Leftrightarrow x=\dfrac{7}{6}\)

\(\left(5\right)\) \(3x\left(2x-1\right)-6x\left(x+2\right)=-3x+4\)

\(\Leftrightarrow6x^2-3x-6x^2-12x=-3x+4\)

\(\Leftrightarrow-15x+3x=4\)

\(\Leftrightarrow-12x=4\)

\(\Leftrightarrow x=-\dfrac{1}{3}\)

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