Question

The fraction
$\frac{2( \sqrt{2} + \sqrt{6} ) }{3( \sqrt{2} + \sqrt{3} )}$
is equal....

$a) \: \frac{2 \sqrt{2} }{3}$
$b) \: \: 1$
$c) \frac{2 \sqrt{3} }{3}$
$d) \frac{4}{3}$
​

Answer 1

Answer:

Subscripts and Superscripts

Subscripts and superscripts (such as exponents) can be made using the underscore _ and carat ^ symbols respectively.

Symbol Command Symbol Command

$2^{2}$ 2^2 $\textstyle a_i$ a_i

$\textstyle 2^{23}$ 2^{23} $\textstyle n_{i-1}$ n_{i-1}

$a^{i+1}_3$ a^{i+1}_3 $x^{3^2}$ x^{3^2}

$2^{a_i}$ 2^{a_i} $2^a_i$ 2^a_i

Notice that we can apply both a subscript and a superscript at the same time. For subscripts or superscripts with more than one character, you must surround with curly braces. For example, x^10 produces $x^10$, while x^{10} produces $x^{10}$.

Math Commands

Here are some commonly used math commands in LaTeX:

Fractions

Symbol Command

$\frac {1}{2}$ \frac{1}{2} or \frac12

$\frac{2}{x+2}$ \frac{2}{x+2}

$\frac{1+\frac{1}{x}}{3x + 2}$ \frac{1+\frac{1}{x}}{3x + 2}

Notice that with fractions with a 1-digit numerator and a 1-digit denominator, we can simply group the numerator and the denominator together as one number. However, for fractions with either a numerator or a denominator that requires more than one character (or if the numerator starts with a letter), you need to surround everything in curly brackets.