a, \(x^2\) + 6x + 5 = 0
=>\(x^2\) + x + 5x +5 = 0
=>x(x + 1) + 5(x + 1) = 0
=>(x + 1)(x + 5) = 0
=> x + 1 =0 hoặc x + 5 =0
=> x = -1 hoặc x = -5
c) \(\dfrac{x+3}{x-1}+\dfrac{2x+5}{x-1}+\dfrac{14-3x}{1-x}\)
\(=\dfrac{x+3}{x-1}+\dfrac{2x+5}{x-1}-\dfrac{14-3x}{x-1}\)
\(=\dfrac{x+3+2x+5-14+3x}{x-1}\)
\(=\dfrac{6x-6}{x-1}\)
\(=\dfrac{6\left(x-1\right)}{x-1}\)
\(=6.\)
d) \(\dfrac{3x}{2y-2x}+\dfrac{3y}{x+y}+\dfrac{3y\left(3y-x\right)}{2\left(x^2-y^2\right)}\)
\(=-\dfrac{3x}{2\left(x-y\right)}+\dfrac{3y}{x+y}+\dfrac{3y\left(3y-x\right)}{2\left(x-y\right)\left(x+y\right)}\)
\(=-\dfrac{3x\left(x+y\right)+6y\left(x-y\right)+3y\left(3y-x\right)}{2\left(x-y\right)\left(x+y\right)}\)
\(=-\dfrac{3x^2+3xy+6xy-6y^2+9y^2-3xy}{2\left(x-y\right)\left(x+y\right)}\)
\(=-\dfrac{3x^2+6xy+3y^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=-\dfrac{3\left(x^2+2xy+y^2\right)}{2\left(x-y\right)\left(x+y\right)}\)
\(=-\dfrac{3\left(x+y\right)^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=-\dfrac{3\left(x+y\right)}{2\left(x-y\right)}\).
1)
\(x^2-6x+5\\ =\left(x^2-x\right)-\left(5x-5\right)\\ =x\left(x-1\right)-5\left(x-1\right)\\ =\left(x-1\right)\left(x-5\right)\)
2.
b)
\(\left(x+3\right)\left(x-2\right)=x^2+x-6\)
d.
\(\dfrac{3x}{2y-2x}+\dfrac{3y}{x+y}+\dfrac{3y\left(3y-x\right)}{2\left(x^2-y^2\right)}\\ =-\dfrac{3x\left(x+y\right)}{2\left(x-y\right)\left(x+y\right)}+\dfrac{3y\left(2x-2y\right)}{2\left(x-y\right)\left(x+y\right)}+\dfrac{3y\left(3y-x\right)}{2\left(x-y\right)\left(x+y\right)}\\ =\dfrac{-3x^2+3xy+6xy-6y^2+9y^2-3xy}{2\left(x^2-y^2\right)}\\ =-\dfrac{3x^2+6xy++3y^2}{2\left(x^2-y^2\right)}\\ =-\dfrac{3\left(x^2+2xy+y^2\right)}{2\left(x^2-y^2\right)}\\ =-\dfrac{3\left(x+y\right)^2}{2\left(x-y\right)\left(x+y\right)}\\ =-\dfrac{3\left(x+y\right)}{2\left(x-y\right)}\)
