The ratio is used for comparing two quantities of the sane kind.

The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be in proportion.

The concept of ratio and proportion is majorly based on ratios and fractions.  

Solution:

(v) ${{x}^{2}}+4x+4$and ${{x}^{2}}-x-6$

Given question can be written as,

$=({{x}^{2}}+4x+4)/({{x}^{2}}-x-6)$

$={{(x+2)}^{2}}/\left[ (x-3)(x+2) \right]$

$=(x+2)/(x-3)$

Therefore, ratio of the given terms is $(x+2):(x-3)$