y2-10y+25y2-2y-35y2-259

Multiply the numerator by the reciprocal of the denominator.

y2-10y+25y2-2y-35⋅9y2-25

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

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

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)

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

Add 1 and 1.

(y-5)⋅9(y-7)(y+5)2

Move 9 to the left of y-5.

9(y-5)(y-7)(y+5)2

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