How to Solve for Variables in Equations with Multiple Variables and Equations?

In summary, fractures are caused by physical force or impact that exceeds the strength of the bone. To prevent fractures, it is important to maintain strong bones through a balanced diet and regular exercise, as well as avoiding high-risk activities. Fractures can be diagnosed through physical examination and imaging tests, and treatment may include immobilization, medication, physical therapy, or surgery. Healing time for fractures varies depending on the type and severity, with simple fractures taking 6-8 weeks to heal and more complex fractures taking several months.
  • #1
proto
5
0
[tex]\frac{1}{x^3(x^2+1)}=\frac{ax^2+bx+c}{x^3}+\frac{dx+e}{x^2}\\[/tex]
[tex]ax^4+bx^3+cx^2+dx^4+ex^3=x^4(a+d)+x^3(b+e)+cx^2=1\\[/tex]
[tex]c=0\\[/tex]
[tex]b+e=0\\[/tex]
[tex]a+d=0\\[/tex]

i got 4 variables with 2 equations

what to do??
 
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  • #2
proto said:
[tex]\frac{1}{x^3(x^2+1)}=\frac{ax^2+bx+c}{x^3}+\frac{dx+e}{x^2}\\[/tex]
[tex]ax^4+bx^3+cx^2+dx^4+ex^3=x^4(a+d)+x^3(b+e)+cx^2=1\\[/tex]
[tex]c=0\\[/tex]
[tex]b+e=0\\[/tex]
[tex]a+d=0\\[/tex]

i got 4 variables with 2 equations

what to do??

[tex]\frac{1}{x^3(x^2+1)}=\frac{ax^2+bx+c}{x^3}+\frac{dx+e}{x^2+1}\\[/tex]
 

Related to How to Solve for Variables in Equations with Multiple Variables and Equations?

1. What causes a fracture?

A fracture is caused by physical force or impact that exceeds the strength of the bone. This can happen due to a fall, sports injury, or other traumatic events.

2. How can I prevent a fracture?

To prevent a fracture, it is important to maintain strong bones through a balanced diet rich in calcium and vitamin D, regular exercise, and avoiding activities with a high risk of falls. Wearing protective gear during sports and being cautious when participating in high-risk activities can also help prevent fractures.

3. How is a fracture diagnosed?

A fracture can be diagnosed through a physical examination, medical history, and imaging tests such as X-rays, CT scans, or MRIs. These tests can help determine the location and severity of the fracture.

4. What is the treatment for a fracture?

The treatment for a fracture depends on the type and severity of the fracture. It may include immobilization with a cast or brace, medication for pain and inflammation, physical therapy, and in severe cases, surgery.

5. How long does it take for a fracture to heal?

The healing time for a fracture varies depending on the type and severity of the fracture, as well as the individual's overall health. Generally, it can take 6-8 weeks for a simple fracture to heal, while more complex fractures may take several months to fully heal.

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