# Simplify ((x+2)/(x-1))÷((x+4)/(x^2+4x-5))

x+2x-1÷x+4×2+4x-5
To divide by a fraction, multiply by its reciprocal.
x+2x-1⋅x2+4x-5x+4
Factor x2+4x-5 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 -5 and whose sum is 4.
-1,5
Write the factored form using these integers.
x+2x-1⋅(x-1)(x+5)x+4
x+2x-1⋅(x-1)(x+5)x+4
Simplify terms.
Cancel the common factor of x-1.
Cancel the common factor.
x+2x-1⋅(x-1)(x+5)x+4
Rewrite the expression.
(x+2)x+5x+4
(x+2)x+5x+4
Multiply x+2 and x+5x+4.
(x+2)(x+5)x+4
(x+2)(x+5)x+4
Simplify ((x+2)/(x-1))÷((x+4)/(x^2+4x-5))