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Least common denominator:
x^4/4+x+2+x^4/4+x+2
((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
sqrt(a)/(4-a)/a^(1/4)/(2-a^(1/2))
factorial(s)/factorial(7)/factorial(s-7)/factorial(factorial(2*s))
Factor polynomial:
x^5+x^7
x1*x2+x1^2*x3^2+x2*x3
2*c^4-4*c^3+2*c
x^2-y^2+x-y
Factor squared:
-y^4-y^2+8
x^2-x*a+4*a^2
3*x^2+5*x-3
-y^2-4*y-3
How do you in partial fractions?:
(a^-2-a/a^-1-1)/(a^2+1)
(1/(s+1))*(1/(s-1))
((p+3)/(p^2-2p))*((4p-8)/(p+3))
(3a^2-12)/(9a^3-72)
How do you in partial fractions?:
((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
Identical expressions
((x^- six - sixty-four)/(four + two *x^- one +x^- two))*(x^ two /(four - four /x+ one /x^ two))-(four *x^ two *(two *x+ one))/(one - two *x)
((x to the power of minus 6 minus 64) divide by (4 plus 2 multiply by x to the power of minus 1 plus x to the power of minus 2)) multiply by (x squared divide by (4 minus 4 divide by x plus 1 divide by x squared )) minus (4 multiply by x squared multiply by (2 multiply by x plus 1)) divide by (1 minus 2 multiply by x)
((x to the power of minus six minus sixty minus four) divide by (four plus two multiply by x to the power of minus one plus x to the power of minus two)) multiply by (x to the power of two divide by (four minus four divide by x plus one divide by x to the power of two)) minus (four multiply by x to the power of two multiply by (two multiply by x plus one)) divide by (one minus two multiply by x)
((x-6-64)/(4+2*x-1+x-2))*(x2/(4-4/x+1/x2))-(4*x2*(2*x+1))/(1-2*x)
x-6-64/4+2*x-1+x-2*x2/4-4/x+1/x2-4*x2*2*x+1/1-2*x
((x^-6-64)/(4+2*x^-1+x^-2))*(x²/(4-4/x+1/x²))-(4*x²*(2*x+1))/(1-2*x)
((x to the power of -6-64)/(4+2*x to the power of -1+x to the power of -2))*(x to the power of 2/(4-4/x+1/x to the power of 2))-(4*x to the power of 2*(2*x+1))/(1-2*x)
((x^-6-64)/(4+2x^-1+x^-2))(x^2/(4-4/x+1/x^2))-(4x^2(2x+1))/(1-2x)
((x-6-64)/(4+2x-1+x-2))(x2/(4-4/x+1/x2))-(4x2(2x+1))/(1-2x)
x-6-64/4+2x-1+x-2x2/4-4/x+1/x2-4x22x+1/1-2x
x^-6-64/4+2x^-1+x^-2x^2/4-4/x+1/x^2-4x^22x+1/1-2x
((x^-6-64) divide by (4+2*x^-1+x^-2))*(x^2 divide by (4-4 divide by x+1 divide by x^2))-(4*x^2*(2*x+1)) divide by (1-2*x)
Similar expressions
((x^-6-64)/(4-2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
((x^-6-64)/(4+2*x^-1+x^+2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
((x^+6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x-1))/(1-2*x)
((x^-6+64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x-1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4+4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))+(4*x^2*(2*x+1))/(1-2*x)
((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1+2*x)
((x^-6-64)/(4+2*x^-1-x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)
((x^-6-64)/(4+2*x^+1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)

Expression simplification/ Least common denominator/ ((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)

Least common denominator ((x^-6-64)/(4+2x^-1+x^-2))(x^2/(4-4/x+1/x^2))-(4x^2(2x+1))/(1-2x)

The solution

You have entered [src]

 1                                    
 -- - 64                              
  6             2          2          
 x             x        4*x *(2*x + 1)
----------*---------- - --------------
    2   1      4   1       1 - 2*x    
4 + - + -- 4 - - + --                 
    x    2     x    2                 
        x          x

$$- \frac{4 x^{2} \left(2 x + 1\right)}{1 - 2 x} + \frac{x^{2}}{\left(4 - \frac{4}{x}\right) + \frac{1}{x^{2}}} \frac{-64 + \frac{1}{x^{6}}}{\left(4 + \frac{2}{x}\right) + \frac{1}{x^{2}}}$$

((x^(-6) - 64)/(4 + 2/x + x^(-2)))*(x^2/(4 - 4/x + 1/(x^2))) - (4*x^2)*(2*x + 1)/(1 - 2*x)

General simplification [src]

1 + 2*x

$$2 x + 1$$

1 + 2*x

Fraction decomposition [src]

1 + 2*x

$$2 x + 1$$

1 + 2*x

Numerical answer [src]

-4.0*x^2*(1.0 + 2.0*x)/(1.0 - 2.0*x) + x^2*(-64.0 + x^(-6))/((4.0 + x^(-2) + 2.0/x)*(4.0 + x^(-2) - 4.0/x))

-4.0*x^2*(1.0 + 2.0*x)/(1.0 - 2.0*x) + x^2*(-64.0 + x^(-6))/((4.0 + x^(-2) + 2.0/x)*(4.0 + x^(-2) - 4.0/x))

Combinatorics [src]

1 + 2*x

$$2 x + 1$$

1 + 2*x

Assemble expression [src]

                          2 /      1 \      
                         x *|-64 + --|      
     2                      |       6|      
  4*x *(1 + 2*x)            \      x /      
- -------------- + -------------------------
     1 - 2*x       /    1    4\ /    1    2\
                   |4 + -- - -|*|4 + -- + -|
                   |     2   x| |     2   x|
                   \    x     / \    x     /

$$\frac{x^{2} \left(-64 + \frac{1}{x^{6}}\right)}{\left(4 - \frac{4}{x} + \frac{1}{x^{2}}\right) \left(4 + \frac{2}{x} + \frac{1}{x^{2}}\right)} - \frac{4 x^{2} \left(2 x + 1\right)}{1 - 2 x}$$

-4*x^2*(1 + 2*x)/(1 - 2*x) + x^2*(-64 + x^(-6))/((4 + x^(-2) - 4/x)*(4 + x^(-2) + 2/x))

Rational denominator [src]

     8       13       12      9      10       14 
  - x  - 32*x   - 16*x   + 2*x  + 4*x   + 64*x   
-------------------------------------------------
 6            /       2      3\ /       2      3\
x *(-1 + 2*x)*\x - 4*x  + 4*x /*\x + 2*x  + 4*x /

$$\frac{64 x^{14} - 32 x^{13} - 16 x^{12} + 4 x^{10} + 2 x^{9} - x^{8}}{x^{6} \left(2 x - 1\right) \left(4 x^{3} - 4 x^{2} + x\right) \left(4 x^{3} + 2 x^{2} + x\right)}$$

(-x^8 - 32*x^13 - 16*x^12 + 2*x^9 + 4*x^10 + 64*x^14)/(x^6*(-1 + 2*x)*(x - 4*x^2 + 4*x^3)*(x + 2*x^2 + 4*x^3))

Trigonometric part [src]

                          2 /      1 \      
                         x *|-64 + --|      
     2                      |       6|      
  4*x *(1 + 2*x)            \      x /      
- -------------- + -------------------------
     1 - 2*x       /    1    4\ /    1    2\
                   |4 + -- - -|*|4 + -- + -|
                   |     2   x| |     2   x|
                   \    x     / \    x     /

$$\frac{x^{2} \left(-64 + \frac{1}{x^{6}}\right)}{\left(4 - \frac{4}{x} + \frac{1}{x^{2}}\right) \left(4 + \frac{2}{x} + \frac{1}{x^{2}}\right)} - \frac{4 x^{2} \left(2 x + 1\right)}{1 - 2 x}$$

-4*x^2*(1 + 2*x)/(1 - 2*x) + x^2*(-64 + x^(-6))/((4 + x^(-2) - 4/x)*(4 + x^(-2) + 2/x))

Combining rational expressions [src]

/        6\                2                                                 
\1 - 64*x /*(1 - 2*x) - 4*x *(1 + 2*x)*(1 + 2*x*(1 + 2*x))*(1 + 4*x*(-1 + x))
-----------------------------------------------------------------------------
               (1 - 2*x)*(1 + 2*x*(1 + 2*x))*(1 + 4*x*(-1 + x))

$$\frac{- 4 x^{2} \left(2 x + 1\right) \left(4 x \left(x - 1\right) + 1\right) \left(2 x \left(2 x + 1\right) + 1\right) + \left(1 - 2 x\right) \left(1 - 64 x^{6}\right)}{\left(1 - 2 x\right) \left(4 x \left(x - 1\right) + 1\right) \left(2 x \left(2 x + 1\right) + 1\right)}$$

((1 - 64*x^6)*(1 - 2*x) - 4*x^2*(1 + 2*x)*(1 + 2*x*(1 + 2*x))*(1 + 4*x*(-1 + x)))/((1 - 2*x)*(1 + 2*x*(1 + 2*x))*(1 + 4*x*(-1 + x)))

Common denominator [src]

1 + 2*x

$$2 x + 1$$

1 + 2*x

Powers [src]

                       2 /      1 \      
                      x *|-64 + --|      
 2                       |       6|      
x *(-4 - 8*x)            \      x /      
------------- + -------------------------
   1 - 2*x      /    1    4\ /    1    2\
                |4 + -- - -|*|4 + -- + -|
                |     2   x| |     2   x|
                \    x     / \    x     /

$$\frac{x^{2} \left(-64 + \frac{1}{x^{6}}\right)}{\left(4 - \frac{4}{x} + \frac{1}{x^{2}}\right) \left(4 + \frac{2}{x} + \frac{1}{x^{2}}\right)} + \frac{x^{2} \left(- 8 x - 4\right)}{1 - 2 x}$$

                          2 /      1 \      
                         x *|-64 + --|      
     2                      |       6|      
  4*x *(1 + 2*x)            \      x /      
- -------------- + -------------------------
     1 - 2*x       /    1    4\ /    1    2\
                   |4 + -- - -|*|4 + -- + -|
                   |     2   x| |     2   x|
                   \    x     / \    x     /

$$\frac{x^{2} \left(-64 + \frac{1}{x^{6}}\right)}{\left(4 - \frac{4}{x} + \frac{1}{x^{2}}\right) \left(4 + \frac{2}{x} + \frac{1}{x^{2}}\right)} - \frac{4 x^{2} \left(2 x + 1\right)}{1 - 2 x}$$

-4*x^2*(1 + 2*x)/(1 - 2*x) + x^2*(-64 + x^(-6))/((4 + x^(-2) - 4/x)*(4 + x^(-2) + 2/x))

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator ((x^-6-64)/(4+2*x^-1+x^-2))*(x^2/(4-4/x+1/x^2))-(4*x^2*(2*x+1))/(1-2*x)

The solution

Least common denominator ((x^-6-64)/(4+2x^-1+x^-2))(x^2/(4-4/x+1/x^2))-(4x^2(2x+1))/(1-2x)