<u>Methods to solve rational equation:</u>
Rational equation:
A rational equation is an equation containing at least one rational expression.
Method 1:
The method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable.
For example,

This can be used for rational equations with polynomials too.
For example,

When the terms in a rational equation have unlike denominators, solving the equation will be as follows



Method 2:
Another way of solving the above equation is by finding least common denominator (LCD)

Factors of 4: 
Factors of 8: 
The LCD of 4 and 8 is 8. So, we have to make the right hand side denominator as 8. This is done by the following step,

we get,

On cancelling 8 on both sides we get,

Hence, these are the ways to solve a rational equation.
Let the number of deluxe that Pacific has be x
the number that Caribbean has will be (x+18)
the number that Mediterranean has will be (3x-25)
total b=number of deluxe in the 3 ships will be:
x+(x+18)+(3x-25)
5x-7=928
5x=928+7
x=935/5
x=187
Hence the Pacific has 187, Caribbean has 187+18=205, Mediterranean has (3*187-25)
=534
Answer:
the answer is 4aX(21+5ax)
Step-by-step explanation:the big x is a multiplication symbol
Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.