Question

janet wants to solve the equation $y + \frac{y^4 - 5}{y^2 - 1} = \frac{y^2 + y + 2}{y + 1}$. what should she multiply both sides of the equation by?
options: $y$, $y + 1$, $y^2 + y + 2$, $y^2 - 1$

Explanation:

Step1: Factor the denominator

Recall the difference of squares: \(y^2 - 1=(y + 1)(y - 1)\). The denominators in the equation are \(y^2-1\) and \(y + 1\).

Step2: Determine the least common denominator (LCD)

The denominators are \(y^2-1=(y + 1)(y - 1)\) and \(y + 1\). The LCD of \((y + 1)(y - 1)\) and \(y + 1\) is \(y^2-1\) (since \(y^2-1\) is a multiple of \(y + 1\)). To eliminate the fractions, we multiply both sides of the equation by the LCD, which is \(y^2-1\).

Answer:

\(y^2 - 1\)