Wednesday, 19 September 2018

Simplifying fraction with square root as denominator

I'm trying to find the integral of:




$$\dfrac {2\sqrt{x} - 3x + x^2}{\sqrt{x}}$$



but I first need to simplify it so I tried dividing by the $\sqrt{x}$ for each of the numbers on the top like so:
$$\dfrac {2\sqrt{x}}{\sqrt{x}}$$



and did the same for the others. For the one above it was easy to see that it just simplifies to $2$. But I am unsure how to do the same for the others for instance $\dfrac {-3x}{\sqrt{x}}$. I know to $-\sqrt{x}$ but i don't know what $-3x - \sqrt{x}$ would come out with?

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