Inequality involving fractions and several variables

In summary, the expression involves positive parameters and a condition where all the letters are less than N and some other conditions are satisfied. Using a computer algebra system is recommended for simplifying this expression.
  • #1
kalish1
99
0
What are some simplified conditions for which:

$$W\bigg(A-\frac{X}{W}\bigg)^3\bigg[X-AW-\frac{AY}{N}(B+D)-\frac{AZ}{N}(C+D+E+F+G)\bigg]+\frac{X}{N}\bigg[Y(A+H)(B+D)+AZ(C+D+E+F+G)\bigg]<0$$

**WHERE:**

All of the letters are positive parameters (not constants) and:

$1.$ $$A,B,C,D,E,F,G,H < N \implies \frac{A}{N},\frac{B}{N},\frac{C}{N},\frac{D}{N},\frac{E}{N},\frac{F}{N},\frac{G}{N},\frac{H}{N} <1 $$

$2.$ $AW>X$

Is this problem tractable by hand, or do I have to use Maple/Matlab to simplify my expression somehow?

I have crossposted this question here as I really need help: Inequality involving fractions and several variables - Math Help Forum

Thanks.
 
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  • #2
Unfortunately, this problem is not tractable by hand and you will need to use a computer algebra system such as Maple or Matlab to simplify the expression. You may also need to make some assumptions about the parameters in order to get a simplified condition.
 

1. What is inequality involving fractions and several variables?

Inequality involving fractions and several variables refers to mathematical expressions that compare the relative magnitudes of fractions with multiple variables. These types of inequalities often involve fractions with different denominators and may also include variables raised to different powers.

2. How can I solve an inequality involving fractions and several variables?

Solving an inequality involving fractions and several variables requires following the same rules as solving any other inequality. Begin by isolating the variable on one side of the inequality sign and simplifying the fractions as much as possible. Then, use the properties of inequalities to manipulate the expression until you have a solution for the variable. Finally, check your solution by plugging it back into the original inequality.

3. What are the common mistakes to avoid when solving inequalities involving fractions and several variables?

One common mistake when solving these types of inequalities is forgetting to find the common denominator before adding or subtracting fractions. Another mistake is not distributing properly when there are variables raised to different powers. It is also important to pay attention to the direction of the inequality sign and how it may change when multiplying or dividing by a negative number.

4. Can inequalities involving fractions and several variables have more than one solution?

Yes, inequalities involving fractions and several variables can have multiple solutions. In fact, there can be an infinite number of solutions depending on the inequality and the variables involved. It is important to check your solution in the original inequality to determine if it is a valid solution.

5. How can inequalities involving fractions and several variables be applied in real life?

Inequalities involving fractions and several variables can be used in many real-life situations, such as calculating the amount of ingredients needed for a recipe, determining the minimum and maximum values of a stock portfolio, or finding the optimal solution for a business problem. These types of inequalities help to compare and analyze different options and make informed decisions.

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