- #1
Lapidus
- 344
- 11
Any help please why the following algebraic identity is true
[tex]\frac{k^2}{k^2-m^2} = 1 + \frac{m^2}{k^2-m^2}[/tex]
thanks
[tex]\frac{k^2}{k^2-m^2} = 1 + \frac{m^2}{k^2-m^2}[/tex]
thanks
Proving Algebraic Identity: $\frac{k^2}{k^2-m^2}$
- Thread starter Lapidus
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In summary, the conversation discusses the algebraic identity \frac{k^2}{k^2-m^2} = 1 + \frac{m^2}{k^2-m^2} and suggests different methods for proving it, such as finding a common denominator, using polynomial division, or multiplying both sides by (k^2-m^2). The conversation also mentions the importance of practice and using textbooks for exercises.
- #2
berkeman
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Lapidus said:
Try putting the two terms on the RHS over a common denominator...
- #3
Lapidus
- 344
- 11
Of course! Thanks, Berkeman
- #4
arildno
Science Advisor
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Alternatively, use polynomial division on LHS. 
- #5
Ivan92
- 201
- 3
Or you can multiply both LHS and RHS by (k2-m2) and cancel out the denominators. Probably the easiest way.
- #6
Lapidus
- 344
- 11
Cool. Now it is more obvios than obvious. Funny, first when I saw it, the equation looked wrong.
Anyway, does anybody know perhaps a good site where there are examples of rearranging and solving algebraic equations (and all the tricks that come along with it)? I know all the rules, but I always liked to have some more practise.
Anyway, does anybody know perhaps a good site where there are examples of rearranging and solving algebraic equations (and all the tricks that come along with it)? I know all the rules, but I always liked to have some more practise.
- #7
Theory4G
- 3
- 0
Ivans92's solution is probably the easiest one but some like the polynomial division as well and are very quick with thes solution . Just practice and youll realize what you like/can best.
- #8
Ivan92
- 201
- 3
What kind of math are you in? If you can, try getting a textbook related to the math course you have. Textbooks will always have exercises, ranging from basic to challenging.
- #9
physiqueper4
- 12
- 0
Shame on you Lapidus ! can 'nt you just do the first simple thing, sum the two and find it!
1. What is an algebraic identity?
An algebraic identity is a mathematical statement that is true for all values of the variables involved. It is a way of expressing the relationship between two or more quantities in a general form.
2. How do you prove an algebraic identity?
To prove an algebraic identity, you need to manipulate the given expression using algebraic rules and properties until it is equivalent to the other side of the identity. This can involve simplifying, expanding, or rearranging terms.
3. What is the purpose of proving algebraic identities?
Proving algebraic identities allows us to verify the validity of mathematical equations and to understand the underlying principles and relationships between different quantities. It is also useful in simplifying complex expressions and solving equations.
4. What are the main steps in proving an algebraic identity?
The main steps in proving an algebraic identity include identifying the given expression, manipulating it using algebraic rules and properties, and showing that it is equivalent to the other side of the identity. It is also important to keep track of any restrictions on the variables.
5. Can you give an example of proving an algebraic identity?
Yes, for example, to prove the identity $\frac{k^2}{k^2-m^2} = \frac{1}{1-\frac{m^2}{k^2}}$, we can start by multiplying the denominator of the left side by $\frac{k^2}{k^2}$ to get $\frac{k^2}{k^2-m^2} = \frac{k^2}{k^2} \cdot \frac{1}{1-\frac{m^2}{k^2}}$. Then, we can simplify to get $\frac{k^2}{k^2-m^2} = \frac{1}{1-\frac{m^2}{k^2}}$, which shows that the two sides are equivalent.
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