Respuesta :

znk

Answer:

[(x+3)(x+2)] /[(2x+3)(x-3)]  

Step-by-step explanation:

 [(2x²+x-6)/(x²-x-6)]/[(4x²-9)/(x²+5x+6)]

= (2x²+x-6)/(x²-x-6) × (x²+5x+6) /(4x²-9)                           Factor

= [(2x-3)(x+2)]/[(x-3)(x+2] × [(x+3)(x+2)] /[(2x+3)(2x-3)]     Cancel terms

= (2x-3)/(x-3) × [(x+3)(x+2)] /[(2x+3)(2x-3)]                        Cancel terms

= [(x+3)(x+2)] /[(2x+3)(x-3)]

gmany

[tex]\dfrac{\frac{2x^2+x-6}{x^2-x-6}}{\frac{4x^2-9}{x^2+5x+6}}=(*)\\---------------------\\2x^2+x-6=2x^2+4x-3x-6=2x(x+2)-3(x+2)=(x+2)(2x-3)\\-----------\\x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3)\\-----------\\x^2+5x+6=x^2+2x+3x+6=x(x+2)+3(x+2)=(x+2)(x+3)\\-----------\\4x^2-9=(2x)^2-3^2=(2x-3)(2x+3)\\----------------------[/tex]

[tex](*)=\dfrac{(x+2)(2x-3)}{(x+2)(x-3)}\cdot\dfrac{(x+2)(x+3)}{(2x-3)(2x+3)}=(**)\\----------------------\\(x+2)-canceled\\(2x-3)-canceled\\----------------------\\(**)=\dfrac{(x+2)(x+3)}{(x-3)(2x+3)}\\\\Answer:\ \boxed{\boxed{\dfrac{(x+2)(x+3)}{(2x+3)(x-3)}}}[/tex]

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