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How to Solve Rational Functions?

TopA rational number is that number which can be expressed as a simple fraction or we can say that a number which can be expressed as a ration is termed as rational number. Just like this a Rational Function is also a Ratio of two Functions. These two Functions are polynomial function. We can write rational function as:
f(x) = p(x) /q(x)
Here p(x and q(x) are two Polynomial Functions and f(x) is a rational number.
We have to remember that the denominator q(x) can never be zero. Zero in denominator gives result as infinite so it is not valid. Let us learn how to solve rational functions?
We should follow a particular approach to solve rational function.
Step 1: First we need two polynomial functions so we can find the solution of rational function.
Just put the two polynomial functions equal to each other. If we are not having the denominator then simply put 1 as the denominator. It will help in solving the equation. For an example, if we have an equation as (a+7) / (a-9) = 6. Here on right side we don’t have any denominator so we can place 1 as the denominator so equation will be(a+7) / (a-9) = 6 / 1.
Step 2: Now we do cross multiplication with the factors which means multiply the numerator of one side with the denominator of other side and vice versa. We get the product of numerator and denominator on both the sides.
Step 3: Now make the factors in polynomial form by multiplying the factors.
Step 4: After this, add and subtract the elements having same degrees.
Step 5: Now we can use any method to solve the equation as Quadratic Formula, factoring, linear equation solution etc. It only depends on the factors.
Step 6: if we want to check whether the values we get, are right or wrong, then we can put these values in the factors and check it.
Note that if we get the denominator as zero by putting a value, then value will not be considered.