Evaluate
\frac{1}{a+\sqrt{3}}
Differentiate w.r.t. a
-\frac{1}{\left(a+\sqrt{3}\right)^{2}}
Quiz
Algebra
5 problems similar to:
\frac { \sqrt { 3 } - a } { ( \sqrt { 3 } - a ) ( \sqrt { 3 } + a ) }
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\frac{1}{a+\sqrt{3}}
Cancel out -a+\sqrt{3} in both numerator and denominator.
\frac{a-\sqrt{3}}{\left(a+\sqrt{3}\right)\left(a-\sqrt{3}\right)}
Rationalize the denominator of \frac{1}{a+\sqrt{3}} by multiplying numerator and denominator by a-\sqrt{3}.
\frac{a-\sqrt{3}}{a^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(a+\sqrt{3}\right)\left(a-\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{a-\sqrt{3}}{a^{2}-3}
The square of \sqrt{3} is 3.
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