# Math Help - Simplification

1. ## Simplification

Hello

How would one get from

$
\frac{x(1-\frac{4}{x})-(x-4\ln(x))}{1-\frac{4}{x}}
$

To

$
\frac{4x(1-\ln(x))}{4-x}
$

2. Hello, macca101!

Did you try any algebra on it?

How would one get from: $\frac{x(1-\frac{4}{x})-(x-4\ln(x))}{1-\frac{4}{x}}$ to $\frac{4x(1-\ln(x))}{4-x}$

Did you simplify the numerator?
. . $x\left[1 - \frac{4}{x}\right] - \left[x - 4\ln(x)\right] \;=$ $\;x - 4 - x + 4\ln(x) \;=\;-4 + 4\ln(x)$

So we have: . $\frac{-4 + 4\ln(x)}{1 - \frac{4}{x}}$

Multiply top and bottom by $x:\;\;\frac{x[-4 + 4\ln(x)]}{x - 4}$

Factor: . $\frac{-4x[1 - \ln(x)]}{-(4 - x)} \;= \;\frac{4x[1 - \ln(x)]}{4 - x}$

3. Originally Posted by Soroban
Hello, macca101!

Did you try any algebra on it?

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Yes I did but got tied up in knots

as usual it's obvious once you know how (kicking myself again)

Thank You