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

x2-25×2-10x+25x+5x-5
Multiply the numerator by the reciprocal of the denominator.
x2-25×2-10x+25⋅x-5x+5
Simplify the numerator.
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
Factor using the perfect square rule.
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
Reduce the expression by cancelling the common factors.
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))