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 December 28th, 2014, 06:32 AM #1 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 Simplify How to simplify this expression? $\displaystyle \frac{1}{x}\cdot \sqrt{4+3x}+\frac{3}{2\sqrt{3x+4}}\cdot\ln x$ I know the answer is $\displaystyle \frac{3x(\ln(x)+2)+8}{2x\sqrt{3x+4}}$. But how? Last edited by skipjack; December 28th, 2014 at 07:48 PM. December 28th, 2014, 07:15 AM #2 Senior Member   Joined: Apr 2014 From: Europa Posts: 584 Thanks: 177 The common denominator is $\displaystyle \ 2x\sqrt{3x+4}$ The first fraction is amplified by $\displaystyle \ 2\sqrt{3x+4}$ and the second fraction is amplified by $\displaystyle \ x$ Thus, we get $\displaystyle \color{blue}{\dfrac{2\sqrt{3x+4}\cdot\sqrt{3x+4}+3 x \ln x}{2x \sqrt{3x+4}}=\dfrac{2(3x+4)+3x \ln x}{2x \sqrt{3x+4}}=\dfrac{2\cdot3x+8+3x \ln x}{2x \sqrt{3x+4}} \\\;\\ =\dfrac{3x(2+ \ln x) + 8}{2x \sqrt{3x+4}}}$ Last edited by skipjack; December 28th, 2014 at 07:51 PM. Tags simplify Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mdocka1 Elementary Math 4 January 19th, 2014 11:51 PM thinkfast Algebra 2 January 27th, 2012 06:51 AM MathematicallyObtuse Algebra 3 December 18th, 2010 05:24 AM MIDI Algebra 8 October 10th, 2010 02:18 PM Shamieh Calculus 2 December 31st, 1969 04:00 PM

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