Hello Friends, in today's class we all are going to discuss about one of the most interesting topic from Maharashtra Board Syllabus which is a bit complex topic that is rational expressions applications, Solutions, and Math Help.
Online learning is the best and the most effective way of learing in today’s scenario.
Online learning not only provide ease of learning but also an interactive way too.
Online help is provided by each portal to help the visitors and make easy for them to learn.
Rational Expressions are as same as any fraction the only difference is that the numerator and dominators are polynomials.
In more simple ways we can term we can define it as rational expression is a ratio of two polynomials.
Example:
2x+8
X4-x2 and x3 +x2+2
But 2-√x is is not a rational expression because the above term is not a polynomial.
5-x
In general ratio of two polynomials p(x) and q(x) can be defined as:(want to Learn about Rational numbers,click here),
f(x) = p(x)
q(x)
where q(x) can’t be zero.
Rational expressions can be of two types
· Proper
· Improper
Which are based on the degree of polynomials.
Now what is degree?
Degree of an expression the highest power on the variable.
Proper Rational Expression are those expression in which degree on the top is always less then the degree in bottom.
Example:
X2+2 and x
X3 -------
Improper Rational Expression are those expression in which the degree on top is greater than the degree in bottom.
Example:
X2+1 and 3x5+2x
X+1 x3+1
Properties of Rational Expression
< >Can have any number of vertical asymptotes.Can’t have more than one horizontal asymptotes.Can have at most one oblique asymptotes.
Solution 4:
x+2 = ( x+2 )
x2+2x-15 ( x+5) ( x-3 )
x = -5 and x = 3 and x = 2
After these solutions I think you all must be able to solve all rational expression with bit of practice and efforts and if anyone want to know about Simplifying rational expressions then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Probability Distribution in the next session here.
Online learning is the best and the most effective way of learing in today’s scenario.
Online learning not only provide ease of learning but also an interactive way too.
Online help is provided by each portal to help the visitors and make easy for them to learn.
Rational Expressions are as same as any fraction the only difference is that the numerator and dominators are polynomials.
In more simple ways we can term we can define it as rational expression is a ratio of two polynomials.
Example:
2x+8
X4-x2 and x3 +x2+2
But 2-√x is is not a rational expression because the above term is not a polynomial.
5-x
In general ratio of two polynomials p(x) and q(x) can be defined as:(want to Learn about Rational numbers,click here),
f(x) = p(x)
q(x)
where q(x) can’t be zero.
Rational expressions can be of two types
· Proper
· Improper
Which are based on the degree of polynomials.
Now what is degree?
Degree of an expression the highest power on the variable.
Proper Rational Expression are those expression in which degree on the top is always less then the degree in bottom.
Example:
X2+2 and x
X3 -------
Improper Rational Expression are those expression in which the degree on top is greater than the degree in bottom.
Example:
X2+1 and 3x5+2x
X+1 x3+1
Properties of Rational Expression
< >Can have any number of vertical asymptotes.Can’t have more than one horizontal asymptotes.Can have at most one oblique asymptotes.
Solution 4:
x+2 = ( x+2 )
x2+2x-15 ( x+5) ( x-3 )
x = -5 and x = 3 and x = 2
After these solutions I think you all must be able to solve all rational expression with bit of practice and efforts and if anyone want to know about Simplifying rational expressions then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Probability Distribution in the next session here.
