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Ta có :
6x = 3x+1-5x+6x-5x+4x-9x+7x
=> 6x+1 = (3x+7x) - (5x+5x) + (6x+4x) - 9x
=> 6x+9x+1 = 10x - 10x + 10x
=> 15x+1 = 10x
=> 10x-15x = 1
=> -5x = 1
=> x = 1 : (-5)
=> x = -1
Vậy x = -1
\(đk:x\ne1\\ \dfrac{x^2+5x}{3x^2-6x+3}:\dfrac{7x+35}{6x-6}\\ =\dfrac{x\left(x+5\right)}{3\left(x^2-2x+1\right)}:\dfrac{7\left(x+5\right)}{6\left(x-1\right)}\\ =\dfrac{x\left(x+5\right)}{3\left(x-1\right)^2}\times\dfrac{6\left(x-1\right)}{7\left(x+5\right)}\\ =\dfrac{2x}{7\left(x-1\right)}\)
\(x^2+5x-6\\ =x^2-x+6x-6\\ =x\left(x-1\right)+6\left(x-1\right)\\ =\left(x+6\right)\left(x-1\right)\\ ---\\ 5x^2+5xy-x-y\\ =x\left(5x-1\right)+y\left(5x-1\right)\\ =\left(5x-1\right)\left(x+y\right)\\ ----\\ 7x-6x^2-2\\ =-6x^2+3x+4x-2\\ =-3x\left(2x-1\right)+2\left(2x-1\right)\\ =\left(2-3x\right)\left(2x-1\right)\)
\(x^2+5x-6=\left(x-1\right)\left(x+6\right)\\ 5x^2+5xy-x-y=\left(5x-1\right)\left(x+y\right)\\ 7x-6x^2-2=\left(3x-2\right)\left(2x-1\right)\)
a: =>x^3-3x^2+3x^2-9x+4x-12+a+12 chia hết cho x-3
=>a+12=0
=>a=-12
b: =>2x^2-6x+5x-15+a+15 chia hết cho x-3
=>a+15=0
=>a=-15
c: =>x^3-2x^2-5x^2+20+a-20 chia hết cho x-2
=>a-20=0
=>a=20
e: =>10x^2-15x+8x-12+a+12 chia hết cho 2x-3
=>a+12=0
=>a=-12
f: =>5x^3-x^2+5x^2-x-5x+1-a-1 chia hết cho 5x-1
=>-a-1=0
=>a=-1
a: =>x^3-3x^2+3x^2-9x+4x-12+a+12 chia hết cho x-3
=>a+12=0
=>a=-12
b: =>2x^2-6x+5x-15+a+15 chia hết cho x-3
=>a+15=0
=>a=-15
c: =>x^3-2x^2-5x^2+20+a-20 chia hết cho x-2
=>a-20=0
=>a=20
e: =>10x^2-15x+8x-12+a+12 chia hết cho 2x-3
=>a+12=0
=>a=-12
f: =>5x^3-x^2+5x^2-x-5x+1-a-1 chia hết cho 5x-1
=>-a-1=0
=>a=-1
5x+6x+7x=18x
\(5x+6x+7x\)
\(=\left(5+6+7\right)x\)
\(=18x\)