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Least common denominator:
tan(x/3)^2*(1+tan(x/3)^2)
tan(x/2)/(x^2+x-2)
tan(x^2)/(x*log(2))-x/(sqrt(x^2)*sqrt(1-x^2))+2*x*(1+tan(x^2)^2)*log(x)/log(2)
tan(x)/(2*tan(x)^2+2)+tan(x)-(3*x)/2
Factor polynomial:
x+9*x
x^8+x^6-92*x^4+9*x^2+81
x^8-x^6-4*x^2-16
x^8-x^6
Factor squared:
y^2-9*y*t-5*t^2
-y^2+9*y*t+3*t^2
-y^2+9*y*b-b^2
-y^2-9*y-4
How do you in partial fractions?:
(x^3+2)/(x^3-4x)
(C^2-5c)/(c^2-25)
(x^(4)-45x^(2)+324)/(x^(2)+3x-18)
x^3/(x-2)
Identical expressions
tan(x/ three)^ two *(one +tan(x/ three)^ two)
tangent of (x divide by 3) squared multiply by (1 plus tangent of (x divide by 3) squared )
tangent of (x divide by three) to the power of two multiply by (one plus tangent of (x divide by three) to the power of two)
tan(x/3)2*(1+tan(x/3)2)
tanx/32*1+tanx/32
tan(x/3)²*(1+tan(x/3)²)
tan(x/3) to the power of 2*(1+tan(x/3) to the power of 2)
tan(x/3)^2(1+tan(x/3)^2)
tan(x/3)2(1+tan(x/3)2)
tanx/321+tanx/32
tanx/3^21+tanx/3^2
tan(x divide by 3)^2*(1+tan(x divide by 3)^2)
Similar expressions
tan(x/3)^2*(1-tan(x/3)^2)

Expression simplification/ Least common denominator/ tan(x/3)^2*(1+tan(x/3)^2)

Least common denominator tan(x/3)^2*(1+tan(x/3)^2)

The solution

You have entered [src]

   2/x\ /       2/x\\
tan |-|*|1 + tan |-||
    \3/ \        \3//

$$\left(\tan^{2}{\left(\frac{x}{3} \right)} + 1\right) \tan^{2}{\left(\frac{x}{3} \right)}$$

tan(x/3)^2*(1 + tan(x/3)^2)

General simplification [src]

   2/x\
tan |-|
    \3/
-------
   2/x\
cos |-|
    \3/

$$\frac{\tan^{2}{\left(\frac{x}{3} \right)}}{\cos^{2}{\left(\frac{x}{3} \right)}}$$

tan(x/3)^2/cos(x/3)^2

Fraction decomposition [src]

tan(x/3)^2 + tan(x/3)^4

$$\tan^{4}{\left(\frac{x}{3} \right)} + \tan^{2}{\left(\frac{x}{3} \right)}$$

   2/x\      4/x\
tan |-| + tan |-|
    \3/       \3/

Powers [src]

                    /                     2\ 
                  2 |    /   I*x    -I*x \ | 
 /   I*x    -I*x \  |    |   ---    -----| | 
 |   ---    -----|  |    |    3       3  | | 
 |    3       3  |  |    \- e    + e     / | 
-\- e    + e     / *|1 - ------------------| 
                    |                    2 | 
                    |     / -I*x     I*x\  | 
                    |     | -----    ---|  | 
                    |     |   3       3 |  | 
                    \     \e      + e   /  / 
---------------------------------------------
                              2              
               / -I*x     I*x\               
               | -----    ---|               
               |   3       3 |               
               \e      + e   /

$$- \frac{\left(- \frac{\left(- e^{\frac{i x}{3}} + e^{- \frac{i x}{3}}\right)^{2}}{\left(e^{\frac{i x}{3}} + e^{- \frac{i x}{3}}\right)^{2}} + 1\right) \left(- e^{\frac{i x}{3}} + e^{- \frac{i x}{3}}\right)^{2}}{\left(e^{\frac{i x}{3}} + e^{- \frac{i x}{3}}\right)^{2}}$$

-(-exp(i*x/3) + exp(-i*x/3))^2*(1 - (-exp(i*x/3) + exp(-i*x/3))^2/(exp(-i*x/3) + exp(i*x/3))^2)/(exp(-i*x/3) + exp(i*x/3))^2

Numerical answer [src]

tan(x/3)^2*(1.0 + tan(x/3)^2)

tan(x/3)^2*(1.0 + tan(x/3)^2)

Common denominator [src]

   2/x\      4/x\
tan |-| + tan |-|
    \3/       \3/

$$\tan^{4}{\left(\frac{x}{3} \right)} + \tan^{2}{\left(\frac{x}{3} \right)}$$

tan(x/3)^2 + tan(x/3)^4

Expand expression [src]

   2/x\      4/x\
tan |-| + tan |-|
    \3/       \3/

$$\tan^{4}{\left(\frac{x}{3} \right)} + \tan^{2}{\left(\frac{x}{3} \right)}$$

tan(x/3)^2 + tan(x/3)^4

Trigonometric part [src]

   2/x\
tan |-|
    \3/
-------
   2/x\
cos |-|
    \3/

$$\frac{\tan^{2}{\left(\frac{x}{3} \right)}}{\cos^{2}{\left(\frac{x}{3} \right)}}$$

   4/pi   x\
csc |-- - -|
    \2    3/
------------
     2/x\   
  csc |-|   
      \3/

$$\frac{\csc^{4}{\left(- \frac{x}{3} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{3} \right)}}$$

        /          2/x\    \
        |       sec |-|    |
   2/x\ |           \3/    |
sec |-|*|1 + --------------|
    \3/ |       2/  pi   x\|
        |    sec |- -- + -||
        \        \  2    3//
----------------------------
          2/  pi   x\       
       sec |- -- + -|       
           \  2    3/

$$\frac{\left(\frac{\sec^{2}{\left(\frac{x}{3} \right)}}{\sec^{2}{\left(\frac{x}{3} - \frac{\pi}{2} \right)}} + 1\right) \sec^{2}{\left(\frac{x}{3} \right)}}{\sec^{2}{\left(\frac{x}{3} - \frac{\pi}{2} \right)}}$$

               2        
  /       2/x\\     2/x\
4*|1 + cot |-|| *cot |-|
  \        \6//      \6/
------------------------
                  4     
    /        2/x\\      
    |-1 + cot |-||      
    \         \6//

$$\frac{4 \left(\cot^{2}{\left(\frac{x}{6} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{x}{6} \right)}}{\left(\cot^{2}{\left(\frac{x}{6} \right)} - 1\right)^{4}}$$

             2        
/       2/x\\     2/x\
|1 + tan |-|| *tan |-|
\        \6//      \3/
----------------------
                 2    
    /       2/x\\     
    |1 - tan |-||     
    \        \6//

$$\frac{\left(\tan^{2}{\left(\frac{x}{6} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{x}{3} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right)^{2}}$$

   2/  pi   x\
cos |- -- + -|
    \  2    3/
--------------
      4/x\    
   cos |-|    
       \3/

$$\frac{\cos^{2}{\left(\frac{x}{3} - \frac{\pi}{2} \right)}}{\cos^{4}{\left(\frac{x}{3} \right)}}$$

       1   
1 + -------
       2/x\
    cot |-|
        \3/
-----------
     2/x\  
  cot |-|  
      \3/

$$\frac{1 + \frac{1}{\cot^{2}{\left(\frac{x}{3} \right)}}}{\cot^{2}{\left(\frac{x}{3} \right)}}$$

            2/x\       
       4*cot |-|       
             \6/       
-----------------------
              4        
/        2/x\\     4/x\
|-1 + cot |-|| *sin |-|
\         \6//      \6/

$$\frac{4 \cot^{2}{\left(\frac{x}{6} \right)}}{\left(\cot^{2}{\left(\frac{x}{6} \right)} - 1\right)^{4} \sin^{4}{\left(\frac{x}{6} \right)}}$$

          2/x\        
       tan |-|        
           \3/        
----------------------
             2        
/       2/x\\     4/x\
|1 - tan |-|| *cos |-|
\        \6//      \6/

$$\frac{\tan^{2}{\left(\frac{x}{3} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right)^{2} \cos^{4}{\left(\frac{x}{6} \right)}}$$

      4/x\    
   sec |-|    
       \3/    
--------------
   2/  pi   x\
sec |- -- + -|
    \  2    3/

$$\frac{\sec^{4}{\left(\frac{x}{3} \right)}}{\sec^{2}{\left(\frac{x}{3} - \frac{\pi}{2} \right)}}$$

           2/x\       
      4*tan |-|       
            \6/       
----------------------
             4        
/       2/x\\     4/x\
|1 - tan |-|| *cos |-|
\        \6//      \6/

$$\frac{4 \tan^{2}{\left(\frac{x}{6} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right)^{4} \cos^{4}{\left(\frac{x}{6} \right)}}$$

   4/x\    2/x\
sec |-|*sin |-|
    \3/     \3/

$$\sin^{2}{\left(\frac{x}{3} \right)} \sec^{4}{\left(\frac{x}{3} \right)}$$

   2/x\
sin |-|
    \3/
-------
   4/x\
cos |-|
    \3/

$$\frac{\sin^{2}{\left(\frac{x}{3} \right)}}{\cos^{4}{\left(\frac{x}{3} \right)}}$$

                  2    
     /       2/x\\     
     |1 + cot |-||     
     \        \6//     
-----------------------
              2        
/        2/x\\     2/x\
|-1 + cot |-|| *cot |-|
\         \6//      \3/

$$\frac{\left(\cot^{2}{\left(\frac{x}{6} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{6} \right)} - 1\right)^{2} \cot^{2}{\left(\frac{x}{3} \right)}}$$

               /       2/  pi   x\\
               |    cos |- -- + -||
   2/  pi   x\ |        \  2    3/|
cos |- -- + -|*|1 + --------------|
    \  2    3/ |          2/x\    |
               |       cos |-|    |
               \           \3/    /
-----------------------------------
                 2/x\              
              cos |-|              
                  \3/

$$\frac{\left(1 + \frac{\cos^{2}{\left(\frac{x}{3} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{3} \right)}}\right) \cos^{2}{\left(\frac{x}{3} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{3} \right)}}$$

          /         4/x\\
          |    4*sin |-||
     4/x\ |          \3/|
4*sin |-|*|1 + ---------|
      \3/ |       2/2*x\|
          |    sin |---||
          \        \ 3 //
-------------------------
           2/2*x\        
        sin |---|        
            \ 3 /

$$\frac{4 \left(\frac{4 \sin^{4}{\left(\frac{x}{3} \right)}}{\sin^{2}{\left(\frac{2 x}{3} \right)}} + 1\right) \sin^{4}{\left(\frac{x}{3} \right)}}{\sin^{2}{\left(\frac{2 x}{3} \right)}}$$

     2/x\   
  sin |-|   
      \3/   
------------
   4/pi   x\
sin |-- + -|
    \2    3/

$$\frac{\sin^{2}{\left(\frac{x}{3} \right)}}{\sin^{4}{\left(\frac{x}{3} + \frac{\pi}{2} \right)}}$$

        /       2/x\\
        |    sin |-||
   2/x\ |        \3/|
sin |-|*|1 + -------|
    \3/ |       2/x\|
        |    cos |-||
        \        \3//
---------------------
          2/x\       
       cos |-|       
           \3/

$$\frac{\left(\frac{\sin^{2}{\left(\frac{x}{3} \right)}}{\cos^{2}{\left(\frac{x}{3} \right)}} + 1\right) \sin^{2}{\left(\frac{x}{3} \right)}}{\cos^{2}{\left(\frac{x}{3} \right)}}$$

        /       2/x\\
        |    sec |-||
   2/x\ |        \3/|
sec |-|*|1 + -------|
    \3/ |       2/x\|
        |    csc |-||
        \        \3//
---------------------
          2/x\       
       csc |-|       
           \3/

$$\frac{\left(1 + \frac{\sec^{2}{\left(\frac{x}{3} \right)}}{\csc^{2}{\left(\frac{x}{3} \right)}}\right) \sec^{2}{\left(\frac{x}{3} \right)}}{\csc^{2}{\left(\frac{x}{3} \right)}}$$

               2        
  /       2/x\\     2/x\
4*|1 + tan |-|| *tan |-|
  \        \6//      \6/
------------------------
                  4     
     /       2/x\\      
     |1 - tan |-||      
     \        \6//

$$\frac{4 \left(\tan^{2}{\left(\frac{x}{6} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{x}{6} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{6} \right)}\right)^{4}}$$

           4/x\       
      4*sin |-|       
            \3/       
----------------------
   2/2*x\    2/pi   x\
sin |---|*sin |-- + -|
    \ 3 /     \2    3/

$$\frac{4 \sin^{4}{\left(\frac{x}{3} \right)}}{\sin^{2}{\left(\frac{2 x}{3} \right)} \sin^{2}{\left(\frac{x}{3} + \frac{\pi}{2} \right)}}$$

           2/x\        
        tan |-|        
            \3/        
-----------------------
              2        
/        2/x\\     4/x\
|-1 + cot |-|| *sin |-|
\         \6//      \6/

$$\frac{\tan^{2}{\left(\frac{x}{3} \right)}}{\left(\cot^{2}{\left(\frac{x}{6} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{6} \right)}}$$

             /       2/pi   x\\
             |    csc |-- - -||
   2/pi   x\ |        \2    3/|
csc |-- - -|*|1 + ------------|
    \2    3/ |         2/x\   |
             |      csc |-|   |
             \          \3/   /
-------------------------------
               2/x\            
            csc |-|            
                \3/

$$\frac{\left(1 + \frac{\csc^{2}{\left(- \frac{x}{3} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{3} \right)}}\right) \csc^{2}{\left(- \frac{x}{3} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{3} \right)}}$$

csc(pi/2 - x/3)^2*(1 + csc(pi/2 - x/3)^2/csc(x/3)^2)/csc(x/3)^2

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How to use it?

Identical expressions

Similar expressions

Least common denominator tan(x/3)^2*(1+tan(x/3)^2)

The solution