Question

Simplify completely: 3b2 – 75 / 3b2 – 27b + 60

Answer 1

`((b+5))/((b-4))`

Explanation:

`(3b^(2)-75)/(3b^(2)-27b + 60)`

`(3(b^(2)-25))/(3(b^(2)-9b + 20))`

Simplify numerator:

where
`(b^(2) -25) = (b-5)(b+5)`

`(3(b-5)(b+5))/(3(b^(2)-9b + 20))`

Simplify denominator:

looking at
`b^(2) - 9b + 20`

where a = 1

b = -9

and c = 20

We are looking for two numbers that sum to -9 and multiply to 20:

-5 + (-4) = -9

-5 * (-4) = 20

so
`b^(2) -9b+20 = (b-5)(b-4)`

insert into denominator:

`(3(b-5)(b+5))/(3(b-4)(b-5))`

remove: 3(b-5) from numerator and denominator:

`((b+5))/((b-4))`