x+2x-1÷x+4×2+4x-5

To divide by a fraction, multiply by its reciprocal.

x+2x-1⋅x2+4x-5x+4

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

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))