# Simplify ((y^2-10y+25)/(y^2-2y-35))/((y^2-25)/9)

y2-10y+25y2-2y-35y2-259
Multiply the numerator by the reciprocal of the denominator.
y2-10y+25y2-2y-35⋅9y2-25
Factor using the perfect square rule.
Rewrite 25 as 52.
y2-10y+52y2-2y-35⋅9y2-25
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅y⋅-5
Simplify.
2ab=-10y
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=y and b=-5.
(y-5)2y2-2y-35⋅9y2-25
(y-5)2y2-2y-35⋅9y2-25
Factor y2-2y-35 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -35 and whose sum is -2.
-7,5
Write the factored form using these integers.
(y-5)2(y-7)(y+5)⋅9y2-25
(y-5)2(y-7)(y+5)⋅9y2-25
Simplify the denominator.
Rewrite 25 as 52.
(y-5)2(y-7)(y+5)⋅9y2-52
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=y and b=5.
(y-5)2(y-7)(y+5)⋅9(y+5)(y-5)
(y-5)2(y-7)(y+5)⋅9(y+5)(y-5)
Simplify terms.
Cancel the common factor of y-5.
Factor y-5 out of (y-5)2.
(y-5)(y-5)(y-7)(y+5)⋅9(y+5)(y-5)
Factor y-5 out of (y+5)(y-5).
(y-5)(y-5)(y-7)(y+5)⋅9(y-5)(y+5)
Cancel the common factor.
(y-5)(y-5)(y-7)(y+5)⋅9(y-5)(y+5)
Rewrite the expression.
y-5(y-7)(y+5)⋅9y+5
y-5(y-7)(y+5)⋅9y+5
Multiply y-5(y-7)(y+5) and 9y+5.
(y-5)⋅9(y-7)(y+5)(y+5)
(y-5)⋅9(y-7)(y+5)(y+5)
Raise y+5 to the power of 1.
(y-5)⋅9(y-7)((y+5)1(y+5))
Raise y+5 to the power of 1.
(y-5)⋅9(y-7)((y+5)1(y+5)1)
Use the power rule aman=am+n to combine exponents.
(y-5)⋅9(y-7)(y+5)1+1