Answer
$$\frac{sqrt(x+h)-sqrtx}{h}=\frac{hqrst}{h}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{sqrt(x+h)-sqrtx}{h}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{qrstx+hqrst-sqrtx}{h} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{hqrst}{h}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{qrst} $ by $ \left( x+h\right) $ $$ \color{blue}{qrst} \cdot \left( x+h\right) = qrstx+hqrst $$ |
| ② | Simplify numerator $$ \, \color{blue}{ \cancel{qrstx}} \,+hqrst \, \color{blue}{ -\cancel{qrstx}} \, = hqrst $$ |
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Simplify Rational Expressions