# Solve this equation

I'm not sure how to approach this type of equation. Can anyone help me out?

Solve the equation:

n/n+3 + 7/n+4 = 1

Cyosis
Homework Helper
You want to get rid of the denominators first, then collect terms.

I'm still stuck I'm afraid. Getting rid of the denominators is easy is thety are the same but as these are different I need help with the method.

Cyosis
Homework Helper
You can bring them under the same denominator by cross multiplying. Hint: what method would you use to add 1/3+1/4 together?

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I would convert them both to a common demoninator, namely 12, so they would be easier to add: 4/12 + 3/12 = 7/12

Cyosis
Homework Helper
Exactly, now apply the same procedure to the two fractions in your equation.

Does that mean that the next stage is to multiply the top and bottom of n/n+3 by 4, (giving 4n/n + 12) and the top and bottom of 7/n+4 by 3 (giving 21/n + 12)? We can then multiply both fractions by n + 12 leaving us with 4n + 21 = 1?
Am I on the right track?

Cyosis
Homework Helper
No, we're not dealing with 1/3 and 1/4 in your equation. Post #5 was just an example. However you must use the same method. Perhaps it is instructive if you tell me exactly how you converted 1/3+ 1/4 into 7/12 (step by step). Then copy that method for denominators n+3 and n+4 instead of 3 and 4.

the LCM of 3 and 4 is 12, so 1/3 and 1/4 can both be expressed as twelfths, namely 4/12 and 3/12.
n+3 + n+4 = 2n + 7. Is that the common denominator I should be using?
maybe 7 + n / 2n + 7?

Cyosis
Homework Helper
Where does n+3+n+4 come from? You don't claim that the common denominator for 1/4+1/3 is 3+4 so why would it be for the exercise at hand. The objective is to find a common denominator so you can add the two fractions together. For numbers you're doing it correctly, however n is just a number therefore n+3 is just a number and n+4 is just a number. The rules of mathematics don't suddenly change when you pick another number.

Perhaps an intermediate step. lets define a=n+3 and b=n+4. Can you add 1/a+1/b together in terms of a and b?

Gringo, the least common MULTIPLE of two numbers is a PRODUCT.
Since "n + 3" and "n + 4" are relatively prime, we must multiply them together to get their LCM. This is analogous to LCM(3,4) = 12 (NOT SEVEN!!!)

If you multiply the entire equation by the LCM/LCD, there will be no more fractions.
(But there will be a quadratic equation to solve...)