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Please fill in the gap to simplify the fraction on the left.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$x+\\var{m}$	=	[[0]]
$(x+\\var{m})(x+\\var{n})$		$x+\\var{n}$

These are equivalent fractions so the same number that multiplied/divided the denominator must also multiply/divide the numerator.

Compare the two denominators, what has happened? We have divided the first denominator by $(x+\\var{m})$ to get the second denominator. The same must be done to the numerator, but something divided by itself is $1$.

The expression $\\displaystyle{\\frac{\\var{p}z}{\\frac{\\var{p}}{\\var{p}z}}}$ can be simplified to [[0]] .

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If we multiply or divide the top and bottom of a fraction by a number (not zero) we get an equivalent fraction. We say equivalent because they represent the same amount of the whole.

Recall $\\frac{1}{2}$ is equivalent to $\\frac{3}{6}$, notice we can multiply the top and bottom of $\\frac{1}{2}$ by 3 to get $\\frac{3}{6}$. Similarly, we can multiply the top and bottom of $\\frac{\\frac{x-3}{2x}}{x+1}$ by $2x$ to get the equivalent fraction $\\frac{x-3}{2x^2+2x}$.

Whenever we have such a 'fraction on a fraction' we want to rewrite the fraction to it is just one fraction. We can do this by multiplying by the denominator of the smaller/inner fraction.

Please fill in the gaps to simplify the fraction on the left.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$\\simplify{{q}x^2y+{r}xy+{s}xy^2}$	=	[[0]]
$\\var{t}xy$		[[1]]

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By looking for common factors, we see that $\\var{common}xy$ is a factor of every term (in the numerator and the denominator), there is also no larger term that is common, we call $\\var{common}xy$ the highest common factor. We divide the numerator and the denominator by the highest common factor to get the simplified fraction.

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