Question

What is the simplified form of y^2+7y+12/y^2-2y-15? Choices:

Answer 1

`(y + 4)/(y - 5)`

Option C is the correct option

Explanation:

`\frac{ {y}^(2) + 7y + 12}{ {y}^(2) - 2y - 15 }`

Write 7y as a sum

`\frac{ {y}^(2) + 4y + 3y + 12}{ {y}^(2) - 2y - 15}`

Write -2y as a difference

`\frac{ {y}^(2) + 4y + 3y + 12}{ {y}^(2) + 3y - 5y - 15}`

Factor out y from the expression

`\frac{y(y + 4) + 3y + 12}{ {y}^(2) + 3y - 5y - 15 }`

Factor out 3 from the expression

`\frac{y(y + 4) + 3(y + 4)}{ {y}^(2) + 3y - 5y - 15 }`

factor out y from the expression

`(y(y + 4) + 3(y + 4))/(y(y + 3) - 5y - 15)`

Factor out -5 from the expression

`(y(y + 4) + 3(y + 4))/(y(y + 3) - 5( y + 3))`

factor out y + 4 from the expression

`((y + 4)(y + 3))/(y(y + 3) - 5(y + 3))`

Factor out y + 3 from the expression

`((y + 4)(y + 3))/((y + 3)(y - 5))`

Reduce the fraction with y + 3

`(y + 4)/(y - 5)`

Hope this helps..

Best regards!!