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

Sep 15, 2017

$\frac{1}{2}$

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:

$\frac{3 x - 21}{6 x - 42} = \frac{3 x - 21}{2 \left(3 x - 21\right)}$

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

$\frac{1}{2}$

Sep 15, 2017

$\frac{1}{2}$

Explanation:

$\frac{3 x - 21}{6 x - 42}$

First we see that both terms in the denominator are divisible by ${2}^{1}$:
$\frac{3 x - 21}{2 \cdot 3 x - 2 \cdot 21}$

Since two is a common factor between the two terms, we can ${\text{factorize them}}^{2}$:
$\frac{3 x - 21}{2 \cdot \left(3 x - 21\right)}$

Simplifying:
$\frac{\cancel{3 x - 21}}{2 \cdot \cancel{3 x - 21}} = \frac{1}{2}$

$\Rightarrow \frac{3 x - 21}{6 x - 42} = \frac{1}{2}$

${.}^{1}$(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 $\rightarrow$ 42 is divisible by 2).
${.}^{2}$ $\left(a x + a y\right) = a \left(x + y\right)$