Solve Rational Equations: example 8.66

Solve: $\frac{y}{y + 6} = \frac{72}{y^{2} - 36} + 4 .$

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.

Solve: $\frac{x}{x + 4} = \frac{32}{x^{2} - 16} + 5 .$

How did it go?


Factor all the denominators, so we can note any value of the variable that would make any denominator zero.
Find the least common denominator. The LCD is $(y - 6) (y + 6)$ .
Clear the fractions.
Simplify.
Simplify.
Solve the resulting equation.




Check.
$y = - 6$ is an extraneous solution.


Factor all the denominators, so we can note any value of the variable that would make any denominator zero.
Find the least common denominator. The LCD is $(y - 6) (y + 6)$ .
Clear the fractions.
Simplify.
Simplify.
Solve the resulting equation.




Check.
$y = - 6$ is an extraneous solution.