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Simplifying Complex Fractions That Contain Addition or Subtraction

Example

Simplify:

Solution

Step 1 Perform any addition or subtraction.
In the numerator, the LCD of the fractions is x(x - 1). In the denominator, the LCD of the fractions is x - 1.
Add the fractions in the numerator. Subtract the fractions in the denominator.
Distribute the 5 in the numerator of the complex fraction.
Distribute the 4 in the denominator of the complex fraction.
Combine like terms.
Step 2 Rewrite the complex fraction using a division symbol, Ã·.
Step 3 Invert the second fraction and change the division symbol, Ã·, to the multiplication symbol, Â·.
Step 4 Factor the numerators and denominators.
Step 5 Cancel all pairs of factors common to the numerators and denominators.
Cancel the common factor, x - 1.
Step 6 Multiply the numerators. Multiply the denominators.

Thus,