Solve Rational Equations: example 8.60

Solve: $1 - \frac{5}{y} = - \frac{6}{y^{2}} .$

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: $1 - \frac{2}{a} = \frac{15}{a^{2}} .$

How did it go?


Note any value of the variable that would make any denominator zero.
Find the least common denominator of all denominators in the equation. The LCD is $y^{2}$ .
Clear the fractions by multiplying both sides of the equation by the LCD.
Distribute.
Multiply.
Solve the resulting equation. First write the quadratic equation in standard form.
Factor.
Use the Zero Product Property.
Solve.
Check.
We did not get 0 as an algebraic solution.


Note any value of the variable that would make any denominator zero.
Find the least common denominator of all denominators in the equation. The LCD is $y^{2}$ .
Clear the fractions by multiplying both sides of the equation by the LCD.
Distribute.
Multiply.
Solve the resulting equation. First write the quadratic equation in standard form.
Factor.
Use the Zero Product Property.
Solve.
Check.
We did not get 0 as an algebraic solution.