Rational Inequalities : - The rational expressions are written in the P(x)/q(x) form where p(x) and q (x) are the polynomials i.e p(x), q(x)∈z(x), and q(x)≠0 are known as rational functions. the set of rational function is denoted by Q (x).
Therefore Q(x) = (p(x))/(q(x)) (where p(x), q(x) ∈z(x) and q(x) ≠0. for, if any a(x)∈z(x), then we can write a(x) as ( a(x))/1, so that a(x)∈z(x) and therefore,(a(x))/1 ∈Q(x);i.e a(x)∈Q(x). The rational function example is given below.
(2x+4)/(x²+5x+8)>0
(ax+b)/(cx+d)<0 p="">
Rational inequalities means the left hand side is not equal to the right hand side of the equation. The inequalities are associated with the linear programming. The step by step procedure to solve the inequalities is given here.
The very first step to solve the inequality problems is to write the equation in the correct form. There are two sides in the equation, left hand side and the right hand side. All the variables are written in the left hand side and zero on the right hand side. The second step is to find the critical values or key. To find this we have to keep the denominator and the numerator equal to zero.
The sign analysis chart is prepared by using the critical values. In this step the number line is divided into the sections. The sign analysis is carried out by assuming left hand side values of x and plugs them in the equation and marks the signs. Now using the sign analysis chart find the section which satisfies the inequality equations.
To write the answer the interval notation is used. Let us solve an example (x + 2) / (x² – 9) < 0. Now put the numerator equal to zero, we get x = -2. By putting the denominator equal to zero we get x = +3 and x = -3. Mark these points on the number line. We get minus three, minus two and plus three on the number line.
Now try minus four, plug the value of x equal to minus four we get – 0.286.
Plug x equal to minus 2.5 we get + 0.1818. Now plug 2 in the equation we get minus zero point eight.
Now we try x equal to plus four which is at the right hand side of the number line. We get plus 0.86. The sign is minus, plus and plus sign. The equation is less than zero. To get less than zero we need all the negative values of the equation.
For x equals to plus three and minus three the equation is undefined. For x equals to minus two the equation is zero. The equation is satisfied by the value of x which is less than minus three. Therefore the answer which is the solution of the equation is minus infinite to minus three.
Rational Expressions Applications : - The equations which do not have equal sign are called the expression. The expressions are used to simplify the equations. The expressions are written to form the conditions of the problems.
According to the direction of the question the expressions are formed to solve a problem.
Therefore Q(x) = (p(x))/(q(x)) (where p(x), q(x) ∈z(x) and q(x) ≠0. for, if any a(x)∈z(x), then we can write a(x) as ( a(x))/1, so that a(x)∈z(x) and therefore,(a(x))/1 ∈Q(x);i.e a(x)∈Q(x). The rational function example is given below.
(2x+4)/(x²+5x+8)>0
(ax+b)/(cx+d)<0 p="">
Rational inequalities means the left hand side is not equal to the right hand side of the equation. The inequalities are associated with the linear programming. The step by step procedure to solve the inequalities is given here.
The very first step to solve the inequality problems is to write the equation in the correct form. There are two sides in the equation, left hand side and the right hand side. All the variables are written in the left hand side and zero on the right hand side. The second step is to find the critical values or key. To find this we have to keep the denominator and the numerator equal to zero.
The sign analysis chart is prepared by using the critical values. In this step the number line is divided into the sections. The sign analysis is carried out by assuming left hand side values of x and plugs them in the equation and marks the signs. Now using the sign analysis chart find the section which satisfies the inequality equations.
To write the answer the interval notation is used. Let us solve an example (x + 2) / (x² – 9) < 0. Now put the numerator equal to zero, we get x = -2. By putting the denominator equal to zero we get x = +3 and x = -3. Mark these points on the number line. We get minus three, minus two and plus three on the number line.
Now try minus four, plug the value of x equal to minus four we get – 0.286.
Plug x equal to minus 2.5 we get + 0.1818. Now plug 2 in the equation we get minus zero point eight.
Now we try x equal to plus four which is at the right hand side of the number line. We get plus 0.86. The sign is minus, plus and plus sign. The equation is less than zero. To get less than zero we need all the negative values of the equation.
For x equals to plus three and minus three the equation is undefined. For x equals to minus two the equation is zero. The equation is satisfied by the value of x which is less than minus three. Therefore the answer which is the solution of the equation is minus infinite to minus three.
Rational Expressions Applications : - The equations which do not have equal sign are called the expression. The expressions are used to simplify the equations. The expressions are written to form the conditions of the problems.
According to the direction of the question the expressions are formed to solve a problem.
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