rylynn86 rylynn86
  • 11-10-2018
  • Mathematics
contestada

What is the sum 4x+1/x+2 + x-1/3x

Respuesta :

gmany
gmany gmany
  • 11-10-2018

Answer:

[tex]\dfrac{4x+1}{x+2}+\dfrac{x-1}{3x}=\dfrac{13x^2+4x-2}{3x^2+6x}[/tex]

Step-by-step explanation:

[tex]Domain:\\x+2\neq0\ \wedge\ 3x\neq0\\\\x\neq-2\ \wedge\ x\neq0[/tex]

[tex]\dfrac{4x+1}{x+2}+\dfrac{x-1}{3x}=\dfrac{(4x+1)(3x)}{(x+2)(3x)}+\dfrac{(x-1)(x+2)}{(3x)(x+2)}\\\\=\dfrac{(4x)(3x)+(1)(3x)+(x)(x)+(x)(2)+(-1)(x)+(-1)(2)}{(3x)(x+2)}\\\\=\dfrac{12x^2+3x+x^2+2x-x-2}{(3x)(x)+(3x)(2)}\\\\=\dfrac{13x^2+4x-2}{3x^2+6x}[/tex]

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