Solve frac{|a-sqrt{b}}{a-2sqrt{ab}+b}

\frac { | a - \sqrt { b } } { a - 2 \sqrt { a b } + b }

Evaluate

\frac{|a-\sqrt{b}|}{-2\sqrt{ab}+a+b}

Differentiate w.r.t. a

\frac{asign(a-\sqrt{b})\sqrt{ab}+bsign(a-\sqrt{b})\sqrt{ab}-|a-\sqrt{b}|\sqrt{ab}-2absign(a-\sqrt{b})+b|a-\sqrt{b}|}{\sqrt{ab}\left(-2\sqrt{ab}+a+b\right)^{2}}

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5 problems similar to:

\frac { | a - \sqrt { b } } { a - 2 \sqrt { a b } + b }

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How do you simplify \displaystyle\frac{{{2}\sqrt{{5}}}}{{{2}\sqrt{{7}}+{3}\sqrt{{3}}}} ?

https://socratic.org/questions/how-do-you-simplify-2sqrt5-2sqrt7-3sqrt3

\displaystyle{\left({4}\sqrt{{{35}}}-{6}\sqrt{{{15}}}\right)} Explanation: \displaystyle\frac{{{2}\sqrt{{{5}}}}}{{{2}\sqrt{{{7}}}+{3}\sqrt{{{3}}}}}=\frac{{{2}\sqrt{{{5}}}}}{{\sqrt{{{28}}}+\sqrt{{{27}}}}}=\frac{{{\left({2}\sqrt{{{5}}}\right)}{\left(\sqrt{{{28}}}-\sqrt{{{27}}}\right)}}}{{{\left(\sqrt{{{28}}}+\sqrt{{{27}}}\right)}{\left(\sqrt{{{28}}}-\sqrt{{{27}}}\right)}}}=\frac{{{4}\sqrt{{{35}}}-{6}\sqrt{{{15}}}}}{{1}}={\left({4}\sqrt{{{35}}}-{6}\sqrt{{{15}}}\right)}

How do you rationalize the denominator and simplify \displaystyle\frac{{{4}\sqrt{{5}}}}{{{3}\sqrt{{5}}+{2}\sqrt{{2}}}} ?

https://socratic.org/questions/how-do-you-rationalize-the-denominator-and-simplify-4sqrt5-3sqrt5-2sqrt2

\displaystyle\frac{{1}}{{37}}{\left({60}-{8}\sqrt{{10}}\right)} Explanation: To rationalize the denominator multiply by \displaystyle{\left({3}\sqrt{{5}}-{2}\sqrt{{2}}\right)} in both ...

How do you rationalize the denominator and simplify \displaystyle\frac{\sqrt{{15}}}{{\sqrt{{15}}-\sqrt{{13}}}} ?

https://socratic.org/questions/how-do-you-rationalize-the-denominator-and-simplify-sqrt15-sqrt15-sqrt13

See a solution process below: Explanation: To rationalize the denominator multiply the fraction by the appropriate form of \displaystyle{1} \displaystyle\frac{{{\left(\sqrt{{{15}}}\right)}+{\left(\sqrt{{{13}}}\right)}}}{{{\left(\sqrt{{{15}}}\right)}+{\left(\sqrt{{{13}}}\right)}}}\times\frac{\sqrt{{{15}}}}{{\sqrt{{{15}}}-\sqrt{{{13}}}}}\Rightarrow ...

How do you rationalize the denominator \displaystyle\frac{{\sqrt{{27}}-\sqrt{{7}}}}{{\sqrt{{21}}-{3}}} ?

https://socratic.org/questions/how-do-you-rationalize-the-denominator-sqrt27-sqrt7-sqrt21-3

Evan Mar 24, 2018 \displaystyle\frac{{\sqrt{{27}}-\sqrt{{7}}}}{{\sqrt{{21}}-{3}}} Multiply both the numerator and denominator with \displaystyle{\left(\sqrt{{21}}+{3}\right)} , ...

How do you divide \displaystyle\frac{{{3}\sqrt{{19}}}}{{\sqrt{{26}}-\sqrt{{6}}}} ?

https://socratic.org/questions/how-do-you-divide-3sqrt19-sqrt26-sqrt6

Gió Apr 4, 2015 I would try rationalizing by multiplying and dividing by \displaystyle\sqrt{{{26}}}+\sqrt{{{6}}} :

Show that \frac{a+b}{2} \geq \sqrt{ab} \geq \frac{2ab}{a+b} [duplicate]

https://math.stackexchange.com/questions/2302726/show-that-fracab2-geq-sqrtab-geq-frac2abab

From AM-GM , \frac {a+b}2\ge\sqrt{ab}\tag{1} Cross-multiplying, \frac 1{\sqrt{ab}}\ge \frac 2{a+b}\\ \frac{\sqrt{ab}}{ab}\ge \frac 2{a+b} \sqrt{ab}\ge \frac {2ab}{a+b}\tag{2} Combining (1),(2) ...

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