Question

Janet wants to solve the equation y+y^2-5/y^2-1=y^2+y+2/y+1 What should she multiply both sides of the equation by?

Answer 1

Best to multiply by (y+1)(y-1) since on one side of the equation you have something divided by (y+1) and on the other something over (y²-1). since (y+1)(y-1) expanded is y²-1 this would work.

Answer 2

She should multiply both sides of the equation by (y - 1)(y + 1)

The equation is given as:

y+y^2-5/y^2-1=y^2+y+2/y+1

Rewrite properly as:

$\frac{y+y^2-5}{y^2-1}=\frac{y^2+y+2}{y+1}$

Express the denominator as a difference of two squares

$\frac{y+y^2-5}{(y - 1)(y +1)}=\frac{y^2+y+2}{y+1}$

Next, multiply both sides of the equation by (y - 1)(y + 1)

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