How to simplify (2÷m+3)+(1÷m) and how to simplify [2÷(x+1)(x+2)+3÷(x+2)(x+3)]

Answer 1

as usual, you need to find the common denominator. Assuming you meant

2/(m+3) + 1/m
the LCD = m(m+3). So, you have

(2m + m+3) / m(m+3)
= (3m+3) / m(m+3)

On the other, I think you have
2/((x+1)(x+2)) + 3/((x+2)(x+3))
so the LCD is (x+1)(x+2)(x+3). That gives you

(2(x+3) + 3(x+1)) / (x+1)(x+2)(x+3)
= (2x+6 + 3x+3) / (x+1)(x+2)(x+3)
= (5x+9) / (x+1)(x+2)(x+3)