3. Solve for x and check.

 

 

To clear denominators we multiply by the smallest common denominator which in this case is (x + 3)(x + 1).

 

 

 

The large parentheses on the left side are there because we had the sum of fractions together before we multiplied. However, these parentheses tell us how to proceed. We multiply the factors in front of the parentheses by both terms inside the parentheses.

 

 

This will clear out all of the denominators. Assemble the surviving factors.

 

 

 

Remove parentheses,

 

 

and combine like terms.

 

 

At this point we see that we have a quadratic. Transpose all of the terms to one side and leave a 0 on the other. In this case, the x2 term is positive on the right, so it would be better to transpose all of the terms to the right leaving a 0 on the left.

 

 

Factor

 

 

and set the factors = 0.

 

 

 

 

Check: Let x = 3. Copy the original equation

 

 

except that where there is an x, substitute a 3.

 

 

 

This reduces

 

 

which checks.

 

 

Let x = -2. Copy the original equation

 

 

except that where there is an x, substitute -2.

 

 

 

or

 

 

which checks

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