Final answer to the problem
$2\sec\left(2x\right)$
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Step-by-step Solution
Specify the solving method
1
Multiply the fraction and term
$\frac{2\sec\left(2x\right)\tan\left(2x\right)+2\sec\left(2x\right)^2}{\sec\left(2x\right)+\tan\left(2x\right)}$
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$\frac{2\sec\left(2x\right)\tan\left(2x\right)+2\sec\left(2x\right)^2}{\sec\left(2x\right)+\tan\left(2x\right)}$
Learn how to solve problems step by step online. Factor the expression 1/(sec(2x)+tan(2x))(2sec(2x)tan(2x)+2sec(2x)^2). Multiply the fraction and term. Factor the polynomial 2\sec\left(2x\right)\tan\left(2x\right)+2\sec\left(2x\right)^2 by it's greatest common factor (GCF): 2\sec\left(2x\right). Simplify the fraction \frac{2\sec\left(2x\right)\left(\tan\left(2x\right)+\sec\left(2x\right)\right)}{\sec\left(2x\right)+\tan\left(2x\right)} by \tan\left(2x\right)+\sec\left(2x\right).
Final answer to the problem
$2\sec\left(2x\right)$