((12y+12)/(5y+25)) * ((3y^2-75)/(8y^2-8))

9(y-5)/10(y-1)

Step-by-step explanation:

If brainiest is earned its greatly Appreciated

9y - 45 / 10y - 10 or 9 ( y - 5) / 10(y - 1)

Step-by-step explanation:

(12y + 12) / (5y + 25) * (3y^2 - 75) / (8y^2 - 8)

Let's pick this expression one after the other

(12y + 12) / (5y + 25)

To solve this, let look for a factor that is common to both figures so as to open the brackets

Like (12y + 12)

12 is common

12(y + 1)

(5y + 25), in this 5 is common

5 ( y + 5)

(12y + 12) / ( 5y + 25) = 12(y +1)/5 (y +5)

Lets pick the second expression

(3y^2 - 75) / (8y^2 - 8)

(3y^2 - 75) , 3 is common

3 (y^2 - 25)

( 8y^2 - 8), 8 is common

8(y^2 - 1)

(3y^2 - 75) / (8y^2 - 8) = 3 (y^2 - 25) / 8(y^2 - 1)

Since weve both simplify both expressions

12( y + 1) / 5( y + 5) * 3(y^2 - 25) / 8(y^2 - 1)

Let's simply 3(y^2 -25)

y^2 - 25 = (y + 5)(y - 5)

And

8(y^2 - 1)

y^2 -1 = ( y + 1)(y - 1)

12( y + 1) / 5(y + 5) * 3(y + 5)(y - 5) / 8 (y + 1)(y - 1)

y + 1 and y + 1 cancels

y + 5 and y + 5 also cancels, leaving

12 / 5 * 3( y - 5) / 8 (y - 1)

We can also multiply 12 * 3(y - 5)

= 36( y - 5)

Also, 5 * 8(y - 1)

= 40( y - 1)

36(y - 5) / 40 ( y - 1)

We can break 36/40, which gives 9/10

So, 9( y - 5) / 10 ( y - 1)

We can open the brackets if we want

9y - 45 / 10y - 10