Solve Rational Equations: exemplo 8.67

Problema e solução em inglês, como no livro original.

Solve: $\frac{x}{2 x - 2} - \frac{2}{3 x + 3} = \frac{5 x^{2} - 2 x + 9}{12 x^{2} - 12} .$

Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.

Sua vez

O Try It do livro logo depois deste exemplo: mesma ideia, outros números. Só a resposta é dada.

Solve: $\frac{y}{5 y - 10} - \frac{5}{3 y + 6} = \frac{2 y^{2} - 19 y + 54}{15 y^{2} - 60} .$

Como foi?


We will start by factoring all denominators, to make it easier to identify extraneous solutions and the LCD.
Note any value of the variable that would make any denominator zero.
Find the least common denominator.The LCD is $12 (x - 1) (x + 1)$
Clear the fractions.
Simplify.
Simplify.
Solve the resulting equation.



Check.
$x = 1$ and $x = - 1$ are extraneous solutions. The equation has no solution.


We will start by factoring all denominators, to make it easier to identify extraneous solutions and the LCD.
Note any value of the variable that would make any denominator zero.
Find the least common denominator.The LCD is $12 (x - 1) (x + 1)$
Clear the fractions.
Simplify.
Simplify.
Solve the resulting equation.



Check.
$x = 1$ and $x = - 1$ are extraneous solutions. The equation has no solution.