Question

me ajudem responder a letra e

Answer 1

letra E

$\frac{ x^{2} +5x+6}{2 x^{2} +6x} = \frac{(x+3)(x+2)}{2x(x+3)} = \frac{x+2}{2x}$

Answer 2

$\dfrac{x^{2}+5x+6}{2x^{2}+6x}\\ \\ \\ =\dfrac{x^{2}+2x+3x+6}{2x\cdot\left(x+3 \right )}\\ \\ \\ =\dfrac{x \cdot \left(x+2 \right )+3\cdot\left(x+2 \right )}{2x\cdot\left(x+3 \right )}\\ \\ \\ =\dfrac{\left(x+2 \right )\cdot\left(x+3 \right )}{2x \cdot \left(x+3 \right )}\\ \\ \\ =\dfrac{x+2}{2x}\\ \\ \\ \\ \boxed{\dfrac{x^{2}+5x+6}{2x^{2}+6x}=\dfrac{x+2}{2x}}$