Simplify Complex Rational Expressions: example 8.51

Simplify: $\frac{\frac{1}{3} + \frac{1}{6}}{\frac{1}{2} - \frac{1}{3}} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: $\frac{\frac{1}{2} + \frac{2}{3}}{\frac{5}{6} + \frac{1}{12}} .$

How did it go?


Simplify the numerator and denominator.
Find the LCD and add the fractions in the numerator. Find the LCD and add the fractions in the denominator.
Simplify the numerator and denominator.
Simplify the numerator and denominator, again.
Rewrite the complex rational expression as a division problem.
Multiply the first times by the reciprocal of the second.
Simplify.


Simplify the numerator and denominator.
Find the LCD and add the fractions in the numerator. Find the LCD and add the fractions in the denominator.
Simplify the numerator and denominator.
Simplify the numerator and denominator, again.
Rewrite the complex rational expression as a division problem.
Multiply the first times by the reciprocal of the second.
Simplify.