Rationalizing: (5s^2-20s+36)/((s-2)(s^2-4s+20))

  • Thread starter gtfitzpatrick
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In summary, rationalizing is the process of simplifying or manipulating a mathematical expression to remove any irrational or complex numbers from the denominator. This is important because it allows for easier solving and avoids errors. To rationalize an expression, you must multiply both the numerator and denominator by the conjugate of the denominator. Common mistakes to avoid include forgetting to multiply both terms and not simplifying the resulting expression. Any type of expression with an irrational or complex denominator can be rationalized, but some may require more steps and techniques.
  • #1
gtfitzpatrick
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(5s[tex]^{2}[/tex]-20s+36)/((s-2)(s[tex]^{2}[/tex]-4s+20)

expanding out i just inputed

EXPAND((5·s^2 - 20·s + 36)/((s - 2)·(s^2 - 4·s + 20)), Rational, s)

but trying to L[tex]^{-1}[/tex] does anyone have any ideas?

i tried

LAPLACE((5·s^2 - 20·s + 36)/((s - 2)·(s^2 - 4·s + 20), t, S)·s  Real (0, ∞)

should i just do it by its parts or can i do it whole?
 
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  • #2
First decompose that expression into partial fractions. Then apply the inverse Laplace transform to the individual fraction expressions. In general that's how you find the inverse Laplace transform for complicated expressions.
 

1. What is rationalizing?

Rationalizing is the process of simplifying or manipulating a mathematical expression to remove any irrational or complex numbers from the denominator. This is done to make the expression easier to work with and solve.

2. How do I rationalize the expression (5s^2-20s+36)/((s-2)(s^2-4s+20))?

To rationalize this expression, you will need to multiply both the numerator and denominator by the conjugate of the denominator, which is (s-2)(s+2). This will result in a simplified expression without any irrational or complex numbers in the denominator.

3. Why is it important to rationalize an expression?

Rationalizing an expression is important because it allows us to solve and work with the expression more easily. It also helps us to avoid division by zero errors and makes the expression look cleaner and more organized.

4. What are the common mistakes to avoid when rationalizing an expression?

One common mistake when rationalizing an expression is forgetting to multiply both the numerator and denominator by the conjugate of the denominator. It is also important to distribute the multiplied terms correctly and simplify the resulting expression.

5. Can I rationalize any type of expression?

Yes, you can rationalize any type of expression, as long as it has a denominator with irrational or complex numbers. However, some expressions may require more steps and techniques to rationalize than others.

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