Question

Simplify the difference.

Answer 1

@jim_thompson5910

Answer 2

You need to put the two fractions over a common denominator. Did you know that you can factorise the denominator of the first fraction to make the process simpler?

Answer 3

im confused ..

Answer 4

what do you get when you factor the first denominator?

Answer 5

-13n^3?

Answer 6

I'll let @jim_thompson5910 help you from now :)

Answer 7

let's factor the numerator first

Answer 8

n^2 - 10n + 24

two numbers that multiply to 24 AND add to -10 are: -6 and -4

so n^2 - 10n + 24 factors to (n - 6)(n - 4)

Answer 9

what does n^2-13n+42 factor to?

Answer 10

7 and 6?

Answer 11

7+6 = 13

but we want -13

Answer 12

so what does that mean?

Answer 13

so -7?

Answer 14

-6 and -7

because

-6 times -7 = 42

AND

-6 plus -7 = -13

Answer 15

this means n^2-13n+42 factors to (n - 6)(n - 7)

Answer 16

oh okay i get it ... then what?

Answer 17

so the first fraction turns into


(n - 6)(n - 4)
-------------
(n - 6)(n - 7)

Answer 18

what cancels?

Answer 19

the (n-6)?

Answer 20

good, so you're left with

n - 4
-----
n - 7

Answer 21

now you have

\[\Large \frac{n-4}{n-7} - \frac{9}{n-7}\]

can you take it from here?

Answer 22

if so, tell me what you get

Answer 23

so its the second equation not n-4 / n-7

Answer 24

what do you get when you simplify

\[\Large \frac{n-4}{n-7} - \frac{9}{n-7}\]

Answer 25

n -4 / n-7