Simplify Complex Rational Expressions: example 8.53

Simplify: $\frac{n - \frac{4 n}{n + 5}}{\frac{1}{n + 5} + \frac{1}{n - 5}} .$

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: $\frac{b - \frac{3 b}{b + 5}}{\frac{2}{b + 5} + \frac{1}{b - 5}} .$

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 numerators.
Subtract the rational expressions in the numerator and add in the denominator. Simplify.
Rewrite as fraction division.
Multiply the first times the reciprocal of the second.
Factor any expressions if possible.
Remove common factors.
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 numerators.
Subtract the rational expressions in the numerator and add in the denominator. Simplify.
Rewrite as fraction division.
Multiply the first times the reciprocal of the second.
Factor any expressions if possible.
Remove common factors.
Simplify.