Friends in this session we will talk all about rational expressions, sometimes an rational expression can have fractions of complex form. This complexity is caused because of polynomials functions which are included in numerator and denominator of the rational expression. So the solution of these complex fractions or rational expressions is not so easy it requires an appropriate way.
Lets have some brief discussion on the way of solving any rational expression, while solving complex fraction the first thing is to reduce the polynomials functions of both numerator and denominator to the lowest form
Reducing the polynomials to the lowest form is done by using factorization process for polynomials. After converting polynomial into their factors the common factor is taken out so that the numerator and denominator is divided by their common factor.
Once all the common factor are eliminated than the value of variables of polynomials function is calculated but one important thing while solving rational expression is that the value of x or variable which is used to form polynomial in denominator can not be such as to make the whole denominator zero.
Let us now explore this way of simplifying rational expressions with example :
normal fraction form is as a/ b, where a is numerator and b is denominator if :
a = x2 – 9
and b = x2 - 16
than find the fraction of x2 – 9/ x2 - 16
the above fraction consist of polynomial functions in its both numerator and denominator which is an rational expression form.
So for solving it first we factorize the polynomial functions:
so a/b = (x + 3) (x -3)/ (x + 4) (x -4)
there is no common factor so the above form is the normalized rational expression.
One thing is clear that the value of x is not be equal to -4 and 4, because if it does then the denominator gets zero and the answer of the expression will be infinity.
Students can take help of online solver provided by TutorVista to learn more about rational expression.