Simplify Complex Rational Expressions: example 8.58

Simplify: $\frac{\frac{y}{y + 1}}{1 + \frac{1}{y - 1}} .$

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: $\frac{\frac{x}{x + 3}}{1 + \frac{1}{x + 3}} .$

How did it go?


Find the LCD of all fractions in the complex rational expression.
The LCD is $(y + 1) (y - 1)$ .
Multiply the numerator and denominator by the LCD.
Distribute in the denominator and simplify.
Simplify.
Simplify the denominator, and leave the numerator factored.

Factor the denominator, and remove factors common with the numerator.
Simplify.


Find the LCD of all fractions in the complex rational expression.
The LCD is $(y + 1) (y - 1)$ .
Multiply the numerator and denominator by the LCD.
Distribute in the denominator and simplify.
Simplify.
Simplify the denominator, and leave the numerator factored.

Factor the denominator, and remove factors common with the numerator.
Simplify.