SOLUTION: I need help with simplifying the following equation: 5/(5a+10)-7/(6a+12) This was the best way that it would let me type it in but basically there are two separate fractions:

Question 366084: I need help with simplifying the following equation:
5/(5a+10)-7/(6a+12)
This was the best way that it would let me type it in but basically there are two separate fractions: 5 over 5a+10 minus 7 over 6a+10.
Thank you!
Found 2 solutions by fractalier, solver91311:
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Let's write it using the program as

Now let's factor both denominators to get

We need to somehow find a common denominator...
We can cancel the fives out in the first term and then multiply top and bottom by 6, and get...
=
=

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I believe that is the expression that you want to simplify. Note that I cannot do precisely what you asked to have done. I cannot simplify the equation. That is because there is no equation. An equation has an equals sign in it -- hence the name. Since you have no equals sign that indicates an equal relationship between two expressions, you do not have an equation.

You have two fractions and you wish to find the sum. Just like adding any other fractions, you find the Lowest Common Denominator, apply it, and then add the numerators. The first step in finding an LCD is to determine the factors that the two denominators have in common. In this case, these two denominators have no factors in common, hence the LCD is simply the product of the two denominators.

Apply the LCD:

Use the Distributive Property to eliminate the parentheses in numerator (we will find it convenient to leave the denominator alone for the time being).

Collect like terms:

Factor out a -1:

Eliminate the factor common to both numerator and denominator:

John

My calculator said it, I believe it, that settles it

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