SOLUTION: Simplify the following rational expression: {{{3/(x+1)+2/(3x)}}}

Question 462560: Simplify the following rational expression:

Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Simplify the following rational expression:

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Notice that I changed the wording of your question. You have given us an algebraic expression (with no equal sign.) In an expression, there is nothing to SOLVE. The variable x can be almost any number.However, we can SIMPLIFY this expression into a single term.
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This might seem like a picky thing, but in the language of mathematics, words are very important. It's best to be a precise as you can!
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So, let's simplify this thing! We have an expression with two terms; both are fractions. In order to add them, we need a common denominator (just like you did when you added fractions in elementary school.)
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An easy way to get a common denominator, it to multiply each term by the other term's denominator over itself. In other words, I multiply the first term by (3x)/(3x) and the second term by (x+1)/(/(x+1).I can do this because I'm really multiplying by a fancy version of one. (any number divided by itself equals one.) Watch what happens:
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Now both terms have the same denominator, so we can add them together.

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We can distribute the 3 and 2 over their parentheses in the numerator.

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We can combine like terms.

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Finally, we use the distributive property to simplify the denominator.

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hope this helps!
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Ms.Figgy
math.in.the.vortex
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