Question

How do you evaluate `\frac { 3x - 21} { 6x - 42}`?

Answer 1

`1/2`

Explanation:

Notice that the denominator is two times the numerator.

Even if you don't notice that, you should notice that you can factor out a 2 from the denominator:

`(3x-21)/(6x-42) = (3x-21)/(2(3x-21))`

And now you've got an identical 3x-21 term in both numerator and denominator that cancels out, giving:

`1/2`

Answer 2

`1/2`

Explanation:

`(3x-21)/(6x-42)`

First we see that both terms in the denominator are divisible by `2^1`:
`(3x-21)/(2*3x-2*21)`

Since two is a common factor between the two terms, we can `"factorize them"^2`:
`(3x-21)/(2*(3x-21))`

Simplifying:
`cancel(3x-21)/(2*cancel(3x-21))=1/2`

`rArr(3x-21)/(6x-42)=1/2`

`.^1`(To know when a number is divisible by 2, you look at the last digit, if it is divisible by 2 then the whole number is divisible by 2; 42 last digit 2 is divisible by 2 `rarr` 42 is divisible by 2).
`.^2` `(ax+ay)=a(x+y)`