Mister Exam

Lang:

Other calculators

How to use it?
Least common denominator:
((x+1)^2*(8*x-4))^(1/3)*(8*(x+1)^2/3+(2+2*x)*(8*x-4)/3)/((x+1)^2*(8*x-4))
a/(a+b)+a^2/(b^2-a^2)
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
sin(x)/(2*(1-cos(x))*sqrt(1+cos(x)))-(sqrt(2)-sqrt(1+cos(x)))*sin(x)/(1-cos(x))^2
Factor polynomial:
x^2+x-2
x^4+x^3
y^3-y
x+x^8/8
Factor squared:
y^4+9*y^2-5
-y^4-8*y^2-8
-y^2-2*y*b+b^2
x^2-x-6
How do you in partial fractions?:
((9*b)/(a-b))*((a^2-a*b)/(54*b))
(z/(z+6)*(z+6))-(z/(z-6)*(z+6))
(a^2-9)/(15+5*a)
b^9*b^7*b^2/(b^3*b^(1^9)*b^8)
How do you in partial fractions?:
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
Identical expressions
z- two / four *z^ two + sixteen *z+ sixteen /(z/ two *z- four -z^ two + four / two *z^ two - eight - two /z^ two + two *z)
z minus 2 divide by 4 multiply by z squared plus 16 multiply by z plus 16 divide by (z divide by 2 multiply by z minus 4 minus z squared plus 4 divide by 2 multiply by z squared minus 8 minus 2 divide by z squared plus 2 multiply by z)
z minus two divide by four multiply by z to the power of two plus sixteen multiply by z plus sixteen divide by (z divide by two multiply by z minus four minus z to the power of two plus four divide by two multiply by z to the power of two minus eight minus two divide by z to the power of two plus two multiply by z)
z-2/4*z2+16*z+16/(z/2*z-4-z2+4/2*z2-8-2/z2+2*z)
z-2/4*z2+16*z+16/z/2*z-4-z2+4/2*z2-8-2/z2+2*z
z-2/4*z²+16*z+16/(z/2*z-4-z²+4/2*z²-8-2/z²+2*z)
z-2/4*z to the power of 2+16*z+16/(z/2*z-4-z to the power of 2+4/2*z to the power of 2-8-2/z to the power of 2+2*z)
z-2/4z^2+16z+16/(z/2z-4-z^2+4/2z^2-8-2/z^2+2z)
z-2/4z2+16z+16/(z/2z-4-z2+4/2z2-8-2/z2+2z)
z-2/4z2+16z+16/z/2z-4-z2+4/2z2-8-2/z2+2z
z-2/4z^2+16z+16/z/2z-4-z^2+4/2z^2-8-2/z^2+2z
z-2 divide by 4*z^2+16*z+16 divide by (z divide by 2*z-4-z^2+4 divide by 2*z^2-8-2 divide by z^2+2*z)
Similar expressions
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2+8-2/z^2+2*z)
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8+2/z^2+2*z)
z-2/4*z^2-16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
z-2/4*z^2+16*z+16/(z/2*z+4-z^2+4/2*z^2-8-2/z^2+2*z)
z-2/4*z^2+16*z+16/(z/2*z-4-z^2-4/2*z^2-8-2/z^2+2*z)
z+2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
z-2/4*z^2+16*z+16/(z/2*z-4+z^2+4/2*z^2-8-2/z^2+2*z)
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2-2*z)
z-2/4*z^2+16*z-16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)

Expression simplification/ Least common denominator/ z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)

Least common denominator z-2/4z^2+16z+16/(z/2z-4-z^2+4/2z^2-8-2/z^2+2*z)

The solution

You have entered [src]

     2                                            
    z                           16                
z - -- + 16*z + ----------------------------------
    2           z          2      2       2       
                -*z - 4 - z  + 2*z  - 8 - -- + 2*z
                2                          2      
                                          z

$$\left(16 z + \left(- \frac{z^{2}}{2} + z\right)\right) + \frac{16}{2 z + \left(\left(\left(2 z^{2} + \left(- z^{2} + \left(z \frac{z}{2} - 4\right)\right)\right) - 8\right) - \frac{2}{z^{2}}\right)}$$

z - z^2/2 + 16*z + 16/((z/2)*z - 4 - z^2 + 2*z^2 - 8 - 2/z^2 + 2*z)

General simplification [src]

  /       /      2 /         2      \\         \
z*\64*z + \-4 + z *\-24 + 3*z  + 4*z//*(34 - z)/
------------------------------------------------
           /      2 /         2      \\         
         2*\-4 + z *\-24 + 3*z  + 4*z//

$$\frac{z \left(64 z + \left(34 - z\right) \left(z^{2} \left(3 z^{2} + 4 z - 24\right) - 4\right)\right)}{2 \left(z^{2} \left(3 z^{2} + 4 z - 24\right) - 4\right)}$$

z*(64*z + (-4 + z^2*(-24 + 3*z^2 + 4*z))*(34 - z))/(2*(-4 + z^2*(-24 + 3*z^2 + 4*z)))

Fraction decomposition [src]

17*z - z^2/2 + 32*z^2/(-4 - 24*z^2 + 3*z^4 + 4*z^3)

$$- \frac{z^{2}}{2} + \frac{32 z^{2}}{3 z^{4} + 4 z^{3} - 24 z^{2} - 4} + 17 z$$

        2                2          
       z             32*z           
17*z - -- + ------------------------
       2             2      4      3
            -4 - 24*z  + 3*z  + 4*z

Rational denominator [src]

   /           3       4             5        2\ 
-z*\136 - 160*z  - 98*z  - 68*z + 3*z  + 816*z / 
-------------------------------------------------
                      2      4      3            
             -8 - 48*z  + 6*z  + 8*z

$$- \frac{z \left(3 z^{5} - 98 z^{4} - 160 z^{3} + 816 z^{2} - 68 z + 136\right)}{6 z^{4} + 8 z^{3} - 48 z^{2} - 8}$$

-z*(136 - 160*z^3 - 98*z^4 - 68*z + 3*z^5 + 816*z^2)/(-8 - 48*z^2 + 6*z^4 + 8*z^3)

Trigonometric part [src]

                                2
          16                   z 
--------------------- + 17*z - --
                    2          2 
      2          3*z             
-12 - -- + 2*z + ----            
       2          2              
      z

$$- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}}$$

16/(-12 - 2/z^2 + 2*z + 3*z^2/2) + 17*z - z^2/2

Assemble expression [src]

                                2
          16                   z 
--------------------- + 17*z - --
                    2          2 
      2          3*z             
-12 - -- + 2*z + ----            
       2          2              
      z

$$- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}}$$

16/(-12 - 2/z^2 + 2*z + 3*z^2/2) + 17*z - z^2/2

Powers [src]

                                2
          16                   z 
--------------------- + 17*z - --
                    2          2 
      2          3*z             
-12 - -- + 2*z + ----            
       2          2              
      z

$$- \frac{z^{2}}{2} + 17 z + \frac{16}{\frac{3 z^{2}}{2} + 2 z - 12 - \frac{2}{z^{2}}}$$

16/(-12 - 2/z^2 + 2*z + 3*z^2/2) + 17*z - z^2/2

Combining rational expressions [src]

  /                /        3      2 /      2\\\
z*\64*z + (34 - z)*\-4 + 4*z  + 3*z *\-8 + z ///
------------------------------------------------
           /        3      2 /      2\\         
         2*\-4 + 4*z  + 3*z *\-8 + z //

$$\frac{z \left(64 z + \left(34 - z\right) \left(4 z^{3} + 3 z^{2} \left(z^{2} - 8\right) - 4\right)\right)}{2 \left(4 z^{3} + 3 z^{2} \left(z^{2} - 8\right) - 4\right)}$$

z*(64*z + (34 - z)*(-4 + 4*z^3 + 3*z^2*(-8 + z^2)))/(2*(-4 + 4*z^3 + 3*z^2*(-8 + z^2)))

Common denominator [src]

        2                2          
       z             32*z           
17*z - -- + ------------------------
       2             2      4      3
            -4 - 24*z  + 3*z  + 4*z

$$- \frac{z^{2}}{2} + \frac{32 z^{2}}{3 z^{4} + 4 z^{3} - 24 z^{2} - 4} + 17 z$$

17*z - z^2/2 + 32*z^2/(-4 - 24*z^2 + 3*z^4 + 4*z^3)

Combinatorics [src]

   /           3       4             5        2\ 
-z*\136 - 160*z  - 98*z  - 68*z + 3*z  + 816*z / 
-------------------------------------------------
             /         2      4      3\          
           2*\-4 - 24*z  + 3*z  + 4*z /

$$- \frac{z \left(3 z^{5} - 98 z^{4} - 160 z^{3} + 816 z^{2} - 68 z + 136\right)}{2 \left(3 z^{4} + 4 z^{3} - 24 z^{2} - 4\right)}$$

-z*(136 - 160*z^3 - 98*z^4 - 68*z + 3*z^5 + 816*z^2)/(2*(-4 - 24*z^2 + 3*z^4 + 4*z^3))

Numerical answer [src]

16.0/(-12.0 + 2.0*z + 1.5*z^2 - 2.0/z^2) + 17.0*z - 0.5*z^2

16.0/(-12.0 + 2.0*z + 1.5*z^2 - 2.0/z^2) + 17.0*z - 0.5*z^2

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)

The solution

Least common denominator z-2/4z^2+16z+16/(z/2z-4-z^2+4/2z^2-8-2/z^2+2*z)