A proportion is a statement that two ratios are equal to each other.
For example 3/6=5/10 (We sometimes read this "3 is to 6 as 5 is to 10".)
There are 4 'numbers' (really number places) involved. If one or more of those 'numbers' is a polynomial, then the proportion becomes a rational equation.
For example: (x-2)/2=7/(x+3) ("x-2 is to 2 as 7 is to x+3").
Typically, once they show up, we want to solve them. (Find the values of x that make them true.)
In the example we would "cross multiply" or multiply both sides by the common denominator (either description applies) to get:
(x-2)(x+3)=2*7. Which is true exactly when
x^2+x-6=14 Which in turn, is equivalent to
x^2+x-20=0 (Subtract 14 on both sides of the equation.)
Solve by factoring (x+5)(x-4)=0
so we need x+5=0 or x-4=0 the first requires
x=-5 and the second x=4.
Notice that we can check our answer:
(-5-2)/2=-7/2 and 7/(-5+3)=7/-2=-7/2. So the ratios on both sides are equal and the statement is true.
