Answer:
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
