# How do you simplify and find the restrictions for (20+40x)/(20x)?

Apr 10, 2017

See the entire explanation below:

#### Explanation:

Factor a $20$ out of each term in the numerator;

$\frac{\left(20 \times 1\right) + \left(20 \times 2 x\right)}{20 x} = \frac{20 \left(1 + 2 x\right)}{20 x}$

Now, cancel the common term in the numerator and denominator:

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{20}}} \left(1 + 2 x\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{20}}} x} = \frac{1 + 2 x}{x}$

Because you cannot divide by $0$ the restriction is $x \ne 0$

Apr 10, 2017

Same thing as the other solution it just looks different.

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

#### Explanation:

I am presenting this solution solely to demonstrate that one situation may take on several forms but still have the same inherent value.

Firstly $x \ne 0$ as the equation becomes 'undefined' at that point.
Basically division by 0 is a definite no no!

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Write as: $\frac{20}{20 x} + \frac{40 x}{20 x}$

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