Question

How do you subtract `\frac { b - 5} { 10b ^ { 2} - 12b } - \frac { 2b - 4} { 10b ^ { 2} - 12b }`?

Answer 1

`(-b-1)/(10b^2-12b)`

Explanation:

`\frac { b - 5} { 10b ^ { 2} - 12b } - \frac { 2b - 4} { 10b ^ { 2} - 12b }`

you already have a common denominator so you just:

`(b-5 -(2b-4))/(10b^2-12b)`

`(b-5 -2b+4)/(10b^2-12b)`

`(-b-1)/(10b^2-12b)`

Answer 2

`(-b-1)/(10b^2-12b)`

Explanation:

`"since the fractions have a "color(blue)"common denominator"`

`"subtract the numerators leaving the denominator"`

`=(b-5-(2b-4))/(10b^2-12b)`

`=(b-5-2b+4)/(10b^2-12b)=(-b-1)/(10b^2-12b)`

Answer 3

`(b-5)/(10b^2-12b)-(2b-4)/(10b^2-12b)=color(blue)((-b-1)/(2b(5b-6)`

Explanation:

Simplify:

`(b-5)/(10b^2-12b)-(2b-4)/(10b^2-12b)`

Since the denominators are the same, we can subtract the numerators.

`(b-5-(2b-4))/(10b^2-12b)`

Simplify `-(2b-4)` to `-2b+4`.

`(b-5-2b+4)/(10b^2-12b)`

Collect like terms in the numerator.

`(b-2b-5+4)/(10b^2-12b)`

Combine like terms.

`(-b-1)/(10b^2-12b)`

Factor out the common `2b` in the denominator.

`(-b-1)/(2b(5b-6)`