1.08  Fractional Equations

College Algebra: One Step at a Time.  Page 130 -133:   #5

NEW PROBLEMS:  #5

Dr. Robert J. Rapalje

Seminole State College of Florida

Sanford, FL  32773

p. 132.  # 5.   

Notice that this is a fractional equation.  The first step is to find the LCD, which is  , and multiply both sides of the equation by the LCD, being careful NOT to allow any of the denominators to be zero.  In other words, in this problem, you must be careful that  and .

This looks pretty ugly, but when you reduce all the fractions, it really is not bad.  In fact, ALL THE DENOMINATORS DIVIDE OUT!!  When you reduce all the fractions, this is what is left—NO FRACTIONS!!

There are at least two ways to solve this.  Probably the easiest is to add  to each side:

Divide both sides by 4:                

Therefore,                                   or  

Both answers are valid, since neither value of x makes the denominator zero.

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