How does $$\frac{3\sqrt{2x-1}-\dfrac{3x+4}{\sqrt{2x-1}}}{2x-1}$$ simplify to $$\frac{3x-7}{(2x-1)^{3/2}}$$
2026-04-24 07:16:59.1777015019
How does $\frac{3\sqrt{2x-1}-\frac{3x+4}{\sqrt{2x-1}}}{2x-1}$ simplify to $\frac{3x-7}{(2x-1)^{3/2}}$?
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$\cfrac {3\sqrt{2x-1}- \cfrac{(3x+4)}{\sqrt{2x-1}}} {2x-1}$
Take $LCM$ of the numerator term.
$\cfrac{\cfrac {3\sqrt{2x-1}(\sqrt{2x-1})- {(3x+4)}}{\sqrt{2x-1}}}{2x-1}$
You get:
$\cfrac{\cfrac {3(2x-1)- {(3x+4)}}{\sqrt{2x-1}}}{2x-1}$
$\cfrac {\cfrac{6x-3- 3x -4}{\sqrt{2x-1}}}{2x-1}$
$\cfrac {\cfrac {3x-7}{\sqrt{2x-1}}}{2x-1}$
And then, the powers add up, by the addition rule of exponents
so the final answer comes out to be :
${\cfrac {3x-7}{{(2x-1)^\frac{3}{2}}}}$