Mister Exam

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Least common denominator:
(z/(z+6)*(z+6))-(z/(z-6)*(z+6))
(z+y*(x*z)/(z^2-x*y)+x*(z*y)/(z^2-x*y)-2*z*((x*z)/(z^2-x*y))*((z*y)/(z^2-x*y)))/(z^2-x*y)
((y-9)/(y-8))*((y^2-64)/(y^2-16*y-64))
((y-9)/(y-8))*((y^2-64)/(y^2-16*y+64))
Factor polynomial:
x^4-x^2
x^4+4
-y^2+y
x^2-y^2+x+y
Factor squared:
x^2+4*x+5
p^4+9*p^2+5
x^2+x+3
y^4-y^2+4
How do you in partial fractions?:
-1/(2*x^2)
(a^3+a)/(a^4+a)
1/(3*sqrt(1-x^2/9))
(z*(z^2+6*z+1)-(4*z*(z+1)))/(z-1)^3+z*(z-1)/(z+1)^3
How do you in partial fractions?:
sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)
Identical expressions
sqrt(a)-(a- one /a^ two)/(sqrt(a)- one /sqrt(a))+(one - one /a^ two)/(sqrt(a)+ one /(sqrt(a)))+ two /a^(three / two)
square root of (a) minus (a minus 1 divide by a squared ) divide by ( square root of (a) minus 1 divide by square root of (a)) plus (1 minus 1 divide by a squared ) divide by ( square root of (a) plus 1 divide by ( square root of (a))) plus 2 divide by a to the power of (3 divide by 2)
square root of (a) minus (a minus one divide by a to the power of two) divide by ( square root of (a) minus one divide by square root of (a)) plus (one minus one divide by a to the power of two) divide by ( square root of (a) plus one divide by ( square root of (a))) plus two divide by a to the power of (three divide by two)
√(a)-(a-1/a^2)/(√(a)-1/√(a))+(1-1/a^2)/(√(a)+1/(√(a)))+2/a^(3/2)
sqrt(a)-(a-1/a2)/(sqrt(a)-1/sqrt(a))+(1-1/a2)/(sqrt(a)+1/(sqrt(a)))+2/a(3/2)
sqrta-a-1/a2/sqrta-1/sqrta+1-1/a2/sqrta+1/sqrta+2/a3/2
sqrt(a)-(a-1/a²)/(sqrt(a)-1/sqrt(a))+(1-1/a²)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)
sqrt(a)-(a-1/a to the power of 2)/(sqrt(a)-1/sqrt(a))+(1-1/a to the power of 2)/(sqrt(a)+1/(sqrt(a)))+2/a to the power of (3/2)
sqrta-a-1/a^2/sqrta-1/sqrta+1-1/a^2/sqrta+1/sqrta+2/a^3/2
sqrt(a)-(a-1 divide by a^2) divide by (sqrt(a)-1 divide by sqrt(a))+(1-1 divide by a^2) divide by (sqrt(a)+1 divide by (sqrt(a)))+2 divide by a^(3 divide by 2)
Similar expressions
sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))-2/a^(3/2)
sqrt(a)-(a-1/a^2)/(sqrt(a)+1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)
sqrt(a)-(a+1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)
sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))-(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)
sqrt(a)+(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)
sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)-1/(sqrt(a)))+2/a^(3/2)
sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1+1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)

Expression simplification/ Least common denominator/ sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)

Least common denominator sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)

The solution

You have entered [src]

                1               1           
            a - --          1 - --          
                 2               2          
  ___           a               a        2  
\/ a  - ------------- + ------------- + ----
          ___     1       ___     1      3/2
        \/ a  - -----   \/ a  + -----   a   
                  ___             ___       
                \/ a            \/ a

$$\left(\frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} + \left(\sqrt{a} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}}\right)\right) + \frac{2}{a^{\frac{3}{2}}}$$

sqrt(a) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a)) + (1 - 1/a^2)/(sqrt(a) + 1/(sqrt(a))) + 2/a^(3/2)

General simplification [src]

$$0$$

Fraction decomposition [src]

$$0$$

Rational denominator [src]

         0          
--------------------
 11                 
a  *(1 + a)*(-1 + a)

$$\frac{0}{a^{11} \left(a - 1\right) \left(a + 1\right)}$$

0/(a^11*(1 + a)*(-1 + a))

Common denominator [src]

$$0$$

Combining rational expressions [src]

        /     3    2         \            /      2\                     
(1 + a)*\1 - a  + a *(-1 + a)/ + (-1 + a)*\-1 + a / + 2*(1 + a)*(-1 + a)
------------------------------------------------------------------------
                          3/2                                           
                         a   *(1 + a)*(-1 + a)

$$\frac{2 \left(a - 1\right) \left(a + 1\right) + \left(a - 1\right) \left(a^{2} - 1\right) + \left(a + 1\right) \left(- a^{3} + a^{2} \left(a - 1\right) + 1\right)}{a^{\frac{3}{2}} \left(a - 1\right) \left(a + 1\right)}$$

((1 + a)*(1 - a^3 + a^2*(-1 + a)) + (-1 + a)*(-1 + a^2) + 2*(1 + a)*(-1 + a))/(a^(3/2)*(1 + a)*(-1 + a))

Powers [src]

                       1           1        
                   1 - --          -- - a   
                        2           2       
  ___    2             a           a        
\/ a  + ---- + ------------- + -------------
         3/2     ___     1       ___     1  
        a      \/ a  + -----   \/ a  - -----
                         ___             ___
                       \/ a            \/ a

$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} + \frac{- a + \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$

                       1               1    
                   1 - --          a - --   
                        2               2   
  ___    2             a               a    
\/ a  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        a      \/ a  + -----   \/ a  - -----
                         ___             ___
                       \/ a            \/ a

$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$

sqrt(a) + 2/a^(3/2) + (1 - 1/a^2)/(sqrt(a) + 1/sqrt(a)) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a))

Numerical answer [src]

a^0.5 + 2.0*a^(-1.5) + (1.0 - 1/a^2)/(a^0.5 + a^(-0.5)) - (a - 1/a^2)/(a^0.5 - a^(-0.5))

a^0.5 + 2.0*a^(-1.5) + (1.0 - 1/a^2)/(a^0.5 + a^(-0.5)) - (a - 1/a^2)/(a^0.5 - a^(-0.5))

Assemble expression [src]

                       1               1    
                   1 - --          a - --   
                        2               2   
  ___    2             a               a    
\/ a  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        a      \/ a  + -----   \/ a  - -----
                         ___             ___
                       \/ a            \/ a

$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$

sqrt(a) + 2/a^(3/2) + (1 - 1/a^2)/(sqrt(a) + 1/sqrt(a)) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a))

Trigonometric part [src]

                       1               1    
                   1 - --          a - --   
                        2               2   
  ___    2             a               a    
\/ a  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        a      \/ a  + -----   \/ a  - -----
                         ___             ___
                       \/ a            \/ a

$$\sqrt{a} + \frac{1 - \frac{1}{a^{2}}}{\sqrt{a} + \frac{1}{\sqrt{a}}} - \frac{a - \frac{1}{a^{2}}}{\sqrt{a} - \frac{1}{\sqrt{a}}} + \frac{2}{a^{\frac{3}{2}}}$$

sqrt(a) + 2/a^(3/2) + (1 - 1/a^2)/(sqrt(a) + 1/sqrt(a)) - (a - 1/a^2)/(sqrt(a) - 1/sqrt(a))

Combinatorics [src]

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Identical expressions

Similar expressions

Least common denominator sqrt(a)-(a-1/a^2)/(sqrt(a)-1/sqrt(a))+(1-1/a^2)/(sqrt(a)+1/(sqrt(a)))+2/a^(3/2)

The solution