Find the LCD them make in into similar:

-3y 4y^2
____ , _____

x-1 x^2-1

Find the LCD then make it into similar:

-3y/x-1 , 4y^2/x^2-1

i just rewrite it but i need your answer

You will need brackets around the denominator to obtain the proper order of operations

your second fraction factors to
4y^2/((x-1)(x+1))

so the LCD is (x-1)(x+1) or the original x^2 - 1

so you have

-3y(x+1)/(x^2 - 1) and 4y^2/(x^2 - 1)

To find the least common denominator (LCD) and make the fractions similar, we need to determine the common factors among all the denominators. In this case, we have the denominators x - 1 and x^2 - 1.

First, let's factorize the denominators:
x - 1 = (x - 1)
x^2 - 1 = (x - 1)(x + 1)

Now, the LCD is the product of all unique factors raised to their highest power. In this case, the common factor is (x - 1). Since (x - 1) is already present in both denominators, we only need to consider (x + 1). Therefore, the LCD is (x - 1)(x + 1).

To make the fractions similar, we need to multiply the numerator and denominator of each fraction by the missing factor(s) from the LCD.

For the first fraction, we need to multiply the numerator and denominator by (x + 1):
-3y / (x - 1) * (x + 1) / (x + 1) = -3y(x + 1) / [(x - 1)(x + 1)]

For the second fraction, we need to multiply the numerator and denominator by (x - 1):
4y^2 / (x^2 - 1) * (x - 1) / (x - 1) = 4y^2(x - 1) / [(x - 1)(x + 1)]

Now, the fractions are similar, and the LCD is (x - 1)(x + 1). The simplified form of the fractions is:
-3y(x + 1) / [(x - 1)(x + 1)], and
4y^2(x - 1) / [(x - 1)(x + 1)]