janet wants to solve the equation $y+\frac{y^{2}-5}{y^{2}-1}=\frac{y^{2}+y + 2}{y + 1}$. what should she…

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

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

Answer

Explanation:

Step1: Factor the denominator

We know that $y^{2}-1=(y + 1)(y - 1)$ by the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$. The denominators in the equation are $y^{2}-1=(y + 1)(y - 1)$ and $y + 1$.

Step2: Find the least common denominator (LCD)

The least common denominator of the fractions in the equation is the product of all the unique factors, each raised to the highest power to which it occurs in any of the denominators. The factors involved are $y - 1$ and $y + 1$. The highest power of $y - 1$ is 1 and the highest power of $y + 1$ is 1. So the LCD is $(y + 1)(y - 1)=y^{2}-1$.

Answer:

B. $y^{2}-1$