b2+5b-36b2

Multiply the numerator by the reciprocal of the denominator.

(b2+5b-36)2b

Multiply b2+5b-36 and 2b.

(b2+5b-36)⋅2b

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 -36 and whose sum is 5.

-4,9

Write the factored form using these integers.

(b-4)(b+9)⋅2b

(b-4)(b+9)⋅2b

Move 2 to the left of (b-4)(b+9).

2(b-4)(b+9)b

Apply the distributive property.

(2b+2⋅-4)(b+9)b

Multiply 2 by -4.

(2b-8)(b+9)b

Apply the distributive property.

2b(b+9)-8(b+9)b

Apply the distributive property.

2b⋅b+2b⋅9-8(b+9)b

Apply the distributive property.

2b⋅b+2b⋅9-8b-8⋅9b

2b⋅b+2b⋅9-8b-8⋅9b

Simplify each term.

Multiply b by b by adding the exponents.

Move b.

2(b⋅b)+2b⋅9-8b-8⋅9b

Multiply b by b.

2b2+2b⋅9-8b-8⋅9b

2b2+2b⋅9-8b-8⋅9b

Multiply 9 by 2.

2b2+18b-8b-8⋅9b

Multiply -8 by 9.

2b2+18b-8b-72b

2b2+18b-8b-72b

Subtract 8b from 18b.

2b2+10b-72b

2b2+10b-72b

Split the fraction 2b2+10b-72b into two fractions.

2b2+10bb+-72b

Split the fraction 2b2+10bb into two fractions.

2b2b+10bb+-72b

Factor b out of 2b2.

b(2b)b+10bb+-72b

Cancel the common factors.

Raise b to the power of 1.

b(2b)b1+10bb+-72b

Factor b out of b1.

b(2b)b⋅1+10bb+-72b

Cancel the common factor.

b(2b)b⋅1+10bb+-72b

Rewrite the expression.

2b1+10bb+-72b

Divide 2b by 1.

2b+10bb+-72b

2b+10bb+-72b

2b+10bb+-72b

Cancel the common factor.

2b+10bb+-72b

Divide 10 by 1.

2b+10+-72b

2b+10+-72b

Move the negative in front of the fraction.

2b+10-72b

Divide (b^2+5b-36)/(b/2)