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Least common denominator:
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
(k1*p*(k4*(t4*p+1))+k2/p)*k5*p+(k1*p)*(k3/(t3*p+1))
a3*b3/a3-a2*b*b2-a2/4*ab2
(x1/3-y1/3)/(x+y)+1/(x2/3-x1/3*y1/3+y2/3)
Factor polynomial:
x^8-4
a^2+8*a+16
u^2+2*u*v+v^2
x^4-81
Factor squared:
2*p^4+p^2-2
y^4-y^2-7
-a^4+8*a^2-1
x^2-x-2
How do you in partial fractions?:
((2*x+10)/(3*x))/(2*x^2+20*x+50*x)
((y-9)/(y-8))*((y^2-64)/(y^2-16*y+64))
(e^(3x)+1)/(e^x+1)
a^3-a^2-a-2/(a^3+1)*a^3-2*a^2+2*a-1/(a^3+a^2+a)*a^2+a/(a^2-3*a+2)
Identical expressions
n*((one +p)^k+p^k*log(p)+(one +p)^k*(k+ one)*log(one +p))/k-n*(p^k+(k+ one)*(one +p)^k)/k^ two
n multiply by ((1 plus p) to the power of k plus p to the power of k multiply by logarithm of (p) plus (1 plus p) to the power of k multiply by (k plus 1) multiply by logarithm of (1 plus p)) divide by k minus n multiply by (p to the power of k plus (k plus 1) multiply by (1 plus p) to the power of k) divide by k squared
n multiply by ((one plus p) to the power of k plus p to the power of k multiply by logarithm of (p) plus (one plus p) to the power of k multiply by (k plus one) multiply by logarithm of (one plus p)) divide by k minus n multiply by (p to the power of k plus (k plus one) multiply by (one plus p) to the power of k) divide by k to the power of two
n*((1+p)k+pk*log(p)+(1+p)k*(k+1)*log(1+p))/k-n*(pk+(k+1)*(1+p)k)/k2
n*1+pk+pk*logp+1+pk*k+1*log1+p/k-n*pk+k+1*1+pk/k2
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k²
n*((1+p) to the power of k+p to the power of k*log(p)+(1+p) to the power of k*(k+1)*log(1+p))/k-n*(p to the power of k+(k+1)*(1+p) to the power of k)/k to the power of 2
n((1+p)^k+p^klog(p)+(1+p)^k(k+1)log(1+p))/k-n(p^k+(k+1)(1+p)^k)/k^2
n((1+p)k+pklog(p)+(1+p)k(k+1)log(1+p))/k-n(pk+(k+1)(1+p)k)/k2
n1+pk+pklogp+1+pkk+1log1+p/k-npk+k+11+pk/k2
n1+p^k+p^klogp+1+p^kk+1log1+p/k-np^k+k+11+p^k/k^2
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p)) divide by k-n*(p^k+(k+1)*(1+p)^k) divide by k^2
Similar expressions
n*((1+p)^k+p^k*log(p)+(1-p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
n*((1+p)^k-p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k+n*(p^k+(k+1)*(1+p)^k)/k^2
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k-1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k-1)*(1+p)^k)/k^2
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1-p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
n*((1-p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k-(k+1)*(1+p)^k)/k^2
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1-p)^k)/k^2
n*((1+p)^k+p^k*log(p)-(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2

Expression simplification/ Least common denominator/ n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2

Least common denominator n((1+p)^k+p^klog(p)+(1+p)^k(k+1)log(1+p))/k-n(p^k+(k+1)(1+p)^k)/k^2

The solution

You have entered [src]

  /       k    k                 k                   \     / k                  k\
n*\(1 + p)  + p *log(p) + (1 + p) *(k + 1)*log(1 + p)/   n*\p  + (k + 1)*(1 + p) /
------------------------------------------------------ - -------------------------
                          k                                           2           
                                                                     k

$$- \frac{n \left(p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{2}} + \frac{n \left(\left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p^{k} \log{\left(p \right)} + \left(p + 1\right)^{k}\right)\right)}{k}$$

(n*((1 + p)^k + p^k*log(p) + ((1 + p)^k*(k + 1))*log(1 + p)))/k - n*(p^k + (k + 1)*(1 + p)^k)/k^2

General simplification [src]

  /   k     /       k    k                 k                   \          k        \
n*\- p  + k*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/ - (1 + p) *(1 + k)/
------------------------------------------------------------------------------------
                                          2                                         
                                         k

$$\frac{n \left(k \left(p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}\right) - p^{k} - \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{2}}$$

n*(-p^k + k*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p)) - (1 + p)^k*(1 + k))/k^2

Numerical answer [src]

n*((1.0 + p)^k + p^k*log(p) + (1.0 + p)^k*(1.0 + k)*log(1 + p))/k - n*(p^k + (1.0 + p)^k*(1.0 + k))/k^2

n*((1.0 + p)^k + p^k*log(p) + (1.0 + p)^k*(1.0 + k)*log(1 + p))/k - n*(p^k + (1.0 + p)^k*(1.0 + k))/k^2

Rational denominator [src]

   2 /       k    k                 k                   \       / k          k        \
n*k *\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/ - k*n*\p  + (1 + p) *(1 + k)/
---------------------------------------------------------------------------------------
                                            3                                          
                                           k

$$\frac{k^{2} n \left(p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}\right) - k n \left(p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{3}}$$

(n*k^2*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p)) - k*n*(p^k + (1 + p)^k*(1 + k)))/k^3

Common denominator [src]

     k            k        k                     k                                   
- n*p  - n*(1 + p)  + k*n*p *log(p) + k*n*(1 + p) *log(1 + p)            k           
------------------------------------------------------------- + n*(1 + p) *log(1 + p)
                               2                                                     
                              k

$$n \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \frac{k n p^{k} \log{\left(p \right)} + k n \left(p + 1\right)^{k} \log{\left(p + 1 \right)} - n p^{k} - n \left(p + 1\right)^{k}}{k^{2}}$$

(-n*p^k - n*(1 + p)^k + k*n*p^k*log(p) + k*n*(1 + p)^k*log(1 + p))/k^2 + n*(1 + p)^k*log(1 + p)

Combinatorics [src]

  /   k          k      k                   k               2        k           \
n*\- p  - (1 + p)  + k*p *log(p) + k*(1 + p) *log(1 + p) + k *(1 + p) *log(1 + p)/
----------------------------------------------------------------------------------
                                         2                                        
                                        k

$$\frac{n \left(k^{2} \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + k p^{k} \log{\left(p \right)} + k \left(p + 1\right)^{k} \log{\left(p + 1 \right)} - p^{k} - \left(p + 1\right)^{k}\right)}{k^{2}}$$

n*(-p^k - (1 + p)^k + k*p^k*log(p) + k*(1 + p)^k*log(1 + p) + k^2*(1 + p)^k*log(1 + p))/k^2

Trigonometric part [src]

  /       k    k                 k                   \     / k          k        \
n*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/   n*\p  + (1 + p) *(1 + k)/
------------------------------------------------------ - -------------------------
                          k                                           2           
                                                                     k

$$\frac{n \left(p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}\right)}{k} - \frac{n \left(p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}\right)}{k^{2}}$$

n*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p))/k - n*(p^k + (1 + p)^k*(1 + k))/k^2

Powers [src]

  /       k    k                 k                   \     / k          k        \
n*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/   n*\p  + (1 + p) *(1 + k)/
------------------------------------------------------ - -------------------------
                          k                                           2           
                                                                     k

n*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p))/k - n*(p^k + (1 + p)^k*(1 + k))/k^2

Combining rational expressions [src]

  /   k     /       k    k                 k                   \          k        \
n*\- p  + k*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/ - (1 + p) *(1 + k)/
------------------------------------------------------------------------------------
                                          2                                         
                                         k

n*(-p^k + k*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p)) - (1 + p)^k*(1 + k))/k^2

Assemble expression [src]

  /       k    k                 k                       k          k        \
  |(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)   p  + (1 + p) *(1 + k)|
n*|-------------------------------------------------- - ---------------------|
  |                        k                                       2         |
  \                                                               k          /

$$n \left(\frac{p^{k} \log{\left(p \right)} + \left(k + 1\right) \left(p + 1\right)^{k} \log{\left(p + 1 \right)} + \left(p + 1\right)^{k}}{k} - \frac{p^{k} + \left(k + 1\right) \left(p + 1\right)^{k}}{k^{2}}\right)$$

  /       k    k                 k                   \     / k          k        \
n*\(1 + p)  + p *log(p) + (1 + p) *(1 + k)*log(1 + p)/   n*\p  + (1 + p) *(1 + k)/
------------------------------------------------------ - -------------------------
                          k                                           2           
                                                                     k

n*((1 + p)^k + p^k*log(p) + (1 + p)^k*(1 + k)*log(1 + p))/k - n*(p^k + (1 + p)^k*(1 + k))/k^2

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Identical expressions

Similar expressions

Least common denominator n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2

The solution

Least common denominator n((1+p)^k+p^klog(p)+(1+p)^k(k+1)log(1+p))/k-n(p^k+(k+1)(1+p)^k)/k^2