# Thread: Simplifying Equations

1. ## Simplifying Equations

Hi,

I know te following equation simplifies as shown, but how?? I also know I should know this but I don't!

$\frac{ (\ln{x})(4x^3)-(x^4)(1/x)} {(ln{x})^2}$

= $\frac{x^3(4\ln{x}-1)}{(\ln{x})^2}$

Many thanks in advance.

2. Originally Posted by fathead05
Hi,

I know te following equation simplifies as shown, but how?? I also know I should know this but I don't!

$\frac{ (\ln{x})(4x^3)-(x^4)(1/x)} {(ln{x})^2}$

= $\frac{x^3(4\ln{x}-1)}{(\ln{x})^2}$

Many thanks in advance.
in the numerator, note that $x^4 \cdot \frac{1}{x} = x^3$

therefore ... $(\ln{x})(4x^3) - x^3 = x^3(4\ln{x} - 1)$

3. Great, thank you.