Question

Add the fractions q/q^2+5q+6 and 1/q^2+3q+2

Answer 1

`\cfrac{q^2+2q+3}{(q+1)(q+2)(q+3)}`

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First, factorize the denominators.

1)

• q² + 5q + 6 =
• q² + 2q + 3q + 6 =
• q(q + 2) + 3(q + 2) =
• (q + 2)(q + 3)

2)

• q² + 3q + 2 =
• q² + q + 2q + 2 =
• q(q + 1) + 2(q + 1) =
• (q + 1)(q + 2)

The common factor of both denominators is q + 2, so the common denominator is:

• (1 + 1)(q + 2)(q + 3)

Now, multiply the fractions by the missing factors and evaluate:

• 
  `\cfrac{q(q+1)}{(q+1)(q+2)(q+3)} +\cfrac{q+3}{(q+1)(q+2)(q+3)} =`
• 
  `\cfrac{q^2+q+q+3}{(q+1)(q+2)(q+3)}=`
• 
  `\cfrac{q^2+2q+3}{(q+1)(q+2)(q+3)}`