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Mathematics I (Math 1132)

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Mathematics I (Math 1132)

Solve Equations Containing Fractions

Depending on the number of terms in the equation, these questions can go from being simple to extremely difficult. Easiest of these types is when you have a single term on the left side and a single term on the right. This of course was discussed earlier in this unit when we looked at equations having fractions, and the technique we use is called cross-multiplication.

However, this method has its limitations when when you have 3 terms, let say:

a38=6a

To solve for a, you can either combine the first two terms together, then cross-multiply (method 1), or find a common denominator – it’s 3 – and multiply each term by 3 to reduce it into an equation without fractions (method 2).

Let’s focus on method 1. Combing the first two terms we get:

a38=a243

Now our equation is suitable for cross-multiplication:

a243=6a136a=a2418a=a2418aa=2417a=24a=2417

Had you gone with method 2, the solution would be the same:

Let’s try another example where method 1 or 2 need to be applied first.

x24=2x426

Starting with method 1, notice that the right side has two terms that can be combined.

=2x426=2x4262=2x4122=2x162

Now the equation becomes:

x24=2x162cross multiply2x2=42x16expand both sides2x4=8x64collect like terms2x8x=64+46x=60solvex=606=10

To see it done using method 2, watch the video below:

Try solving this last example on your own before continuing to another related concept involving algebraic fractions.

3x52=2x13+4
Answer

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Solving fractions when the variable’s in the denominator

Unlike previous examples, the ones you’ll see here have variables in the denominator position. Again, both methods work, but the video shows method 2 only which involves finding the lowest common denominator (LCD). Once the LCD is determined, you multiple the whole equation by the LCD – this will eliminate the every denominator.


Just as you saw when you first simplified expressions through factoring, you may need to do the same when dealing with equations. This is why you learned it with simple expressions first before incorporating the concept to solving.

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