Algebraic Division?

Question

Would you please explain to me the answer to this problem.

x^2 - x - 6/ x^2 + 2x - 15
divided by
x^2 - 4x - 5/ x^2 - 25

remember to recipricate the second one

thank you

Answer 1

x^2-x-6
=x^2+2x-3x-6
=x(x+2)-3(x+2)
=(x+2)(x-3)
x^2+2x-15
=x^2+5x-3x-15
=x(x+5)-3(x+5)
=(x+5)(x-3)
x^2-4x-5
=x^2+x-5x-5
=x(x+1)-5(x+1)
=(x+1)(x-5)
x^2-25
=(x)^2-(5)^2
=(x+5)(x-5)
Therefore given expression
=(x+2)(x-3)/(x+5)(x-3) divided by
(x+1)(x-5)/(x+5)(x-5)
=(x+2)/(x+5) divided by (x+1)/(x+5)
=(x+2)/(x+5) X(x+5)/(x+1)
=(x+2)/(x+1) ans

Answer 2

Factoring:
(x-3)(x+2)/(x+5)(x-3) / (x-5)(x+1)/(x-5)(x-5)

Canceling:
(x+2)/(x+5) / (x+1)/(x-5)

Flip the denominator:
(x+2)(x-5) / (x+5)(x+1)

Answer 3

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