x2-25×2-10x+25x+5x-5

Multiply the numerator by the reciprocal of the denominator.

x2-25×2-10x+25⋅x-5x+5

Rewrite 25 as 52.

x2-52×2-10x+25⋅x-5x+5

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=5.

(x+5)(x-5)x2-10x+25⋅x-5x+5

(x+5)(x-5)x2-10x+25⋅x-5x+5

Rewrite 25 as 52.

(x+5)(x-5)x2-10x+52⋅x-5x+5

Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.

2ab=2⋅x⋅-5

Simplify.

2ab=-10x

Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=x and b=-5.

(x+5)(x-5)(x-5)2⋅x-5x+5

(x+5)(x-5)(x-5)2⋅x-5x+5

Cancel the common factor of x+5.

Cancel the common factor.

(x+5)(x-5)(x-5)2⋅x-5x+5

Rewrite the expression.

x-5(x-5)2(x-5)

x-5(x-5)2(x-5)

Cancel the common factor of x-5.

Factor x-5 out of (x-5)2.

x-5(x-5)(x-5)(x-5)

Cancel the common factor.

x-5(x-5)(x-5)(x-5)

Rewrite the expression.

x-5x-5

x-5x-5

Cancel the common factor of x-5.

Cancel the common factor.

x-5x-5

Divide 1 by 1.

1

1

1

Simplify ((x^2-25)/(x^2-10x+25))/((x+5)/(x-5))