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Least common denominator:
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b)))/(a-b)+(2*sqrt(b))/(sqrt(a)+sqrt(b))
sqrt(b^2*((1-(b^2-a^2)/(b^2+a^2))^2+(2*a-b*sqrt(1-((b-a)*(b+a)/(b^2+a^2))^2)^2)))
(n/((p-4)*(p-4)))-(8/((4-p)*(4-p)))
m-4/m-m-3/m+1
Factor polynomial:
x^4-3*x
x^4/2-x-x^2/2
x^4-2*x-6*x^2+5*x+2
x^4-2*x+4*x^2
Factor squared:
x^2-x*t+t^2
x^2-x*a+12*a^2
-x^2+x+8
-x^2-x*b+15*b^2
How do you in partial fractions?:
1/(x^4+x^2)
x^2/(1-x^4)
(w*i*0.00005)/(1+w*i*0.00005)
w^2/(w-6)-12*w-36/(w-6)
How do you in partial fractions?:
log((2*x-6^(3/2)+16)/(2*x+6^(3/2)+16))/6^(3/2)
Identical expressions
log((two *x- six ^(three / two)+ sixteen)/(two *x+ six ^(three / two)+ sixteen))/ six ^(three / two)
logarithm of ((2 multiply by x minus 6 to the power of (3 divide by 2) plus 16) divide by (2 multiply by x plus 6 to the power of (3 divide by 2) plus 16)) divide by 6 to the power of (3 divide by 2)
logarithm of ((two multiply by x minus six to the power of (three divide by two) plus sixteen) divide by (two multiply by x plus six to the power of (three divide by two) plus sixteen)) divide by six to the power of (three divide by two)
log((2*x-6(3/2)+16)/(2*x+6(3/2)+16))/6(3/2)
log2*x-63/2+16/2*x+63/2+16/63/2
log((2x-6^(3/2)+16)/(2x+6^(3/2)+16))/6^(3/2)
log((2x-6(3/2)+16)/(2x+6(3/2)+16))/6(3/2)
log2x-63/2+16/2x+63/2+16/63/2
log2x-6^3/2+16/2x+6^3/2+16/6^3/2
log((2*x-6^(3 divide by 2)+16) divide by (2*x+6^(3 divide by 2)+16)) divide by 6^(3 divide by 2)
Similar expressions
log((2*x-6^(3/2)+16)/(2*x+6^(3/2)-16))/6^(3/2)
log((2*x+6^(3/2)+16)/(2*x+6^(3/2)+16))/6^(3/2)
log((2*x-6^(3/2)-16)/(2*x+6^(3/2)+16))/6^(3/2)
log((2*x-6^(3/2)+16)/(2*x-6^(3/2)+16))/6^(3/2)

Expression simplification/ Least common denominator/ log((2*x-6^(3/2)+16)/(2*x+6^(3/2)+16))/6^(3/2)

Least common denominator log((2x-6^(3/2)+16)/(2x+6^(3/2)+16))/6^(3/2)

The solution

You have entered [src]

   /       3/2     \
   |2*x - 6    + 16|
log|---------------|
   |       3/2     |
   \2*x + 6    + 16/
--------------------
         3/2        
        6

$$\frac{\log{\left(\frac{\left(2 x - 6^{\frac{3}{2}}\right) + 16}{\left(2 x + 6^{\frac{3}{2}}\right) + 16} \right)}}{6^{\frac{3}{2}}}$$

log((2*x - 6^(3/2) + 16)/(2*x + 6^(3/2) + 16))/6^(3/2)

Fraction decomposition [src]

sqrt(6)*log(16/(16 + 2*x + 6*sqrt(6)) - 6*sqrt(6)/(16 + 2*x + 6*sqrt(6)) + 2*x/(16 + 2*x + 6*sqrt(6)))/36

$$\frac{\sqrt{6} \log{\left(\frac{2 x}{2 x + 6 \sqrt{6} + 16} - \frac{6 \sqrt{6}}{2 x + 6 \sqrt{6} + 16} + \frac{16}{2 x + 6 \sqrt{6} + 16} \right)}}{36}$$

         /                              ___                           \
  ___    |        16                6*\/ 6                 2*x        |
\/ 6 *log|------------------ - ------------------ + ------------------|
         |               ___                  ___                  ___|
         \16 + 2*x + 6*\/ 6    16 + 2*x + 6*\/ 6    16 + 2*x + 6*\/ 6 /
-----------------------------------------------------------------------
                                   36

General simplification [src]

         /            ___\
  ___    |8 + x - 3*\/ 6 |
\/ 6 *log|---------------|
         |            ___|
         \8 + x + 3*\/ 6 /
--------------------------
            36

$$\frac{\sqrt{6} \log{\left(\frac{x - 3 \sqrt{6} + 8}{x + 3 \sqrt{6} + 8} \right)}}{36}$$

sqrt(6)*log((8 + x - 3*sqrt(6))/(8 + x + 3*sqrt(6)))/36

Combinatorics [src]

         /                              ___                           \
  ___    |        16                6*\/ 6                 2*x        |
\/ 6 *log|------------------ - ------------------ + ------------------|
         |               ___                  ___                  ___|
         \16 + 2*x + 6*\/ 6    16 + 2*x + 6*\/ 6    16 + 2*x + 6*\/ 6 /
-----------------------------------------------------------------------
                                   36

$$\frac{\sqrt{6} \log{\left(\frac{2 x}{2 x + 6 \sqrt{6} + 16} - \frac{6 \sqrt{6}}{2 x + 6 \sqrt{6} + 16} + \frac{16}{2 x + 6 \sqrt{6} + 16} \right)}}{36}$$

sqrt(6)*log(16/(16 + 2*x + 6*sqrt(6)) - 6*sqrt(6)/(16 + 2*x + 6*sqrt(6)) + 2*x/(16 + 2*x + 6*sqrt(6)))/36

Numerical answer [src]

0.0680413817439772*log((2*x - 6^(3/2) + 16)/(2*x + 6^(3/2) + 16))

0.0680413817439772*log((2*x - 6^(3/2) + 16)/(2*x + 6^(3/2) + 16))

Rational denominator [src]

         /  /            ___\\
  ___    |2*\8 + x - 3*\/ 6 /|
\/ 6 *log|-------------------|
         |         3/2       |
         \  2*x + 6    + 16  /
------------------------------
              36

$$\frac{\sqrt{6} \log{\left(\frac{2 \left(x - 3 \sqrt{6} + 8\right)}{\left(2 x + 6^{\frac{3}{2}}\right) + 16} \right)}}{36}$$

sqrt(6)*log(2*(8 + x - 3*sqrt(6))/(2*x + 6^(3/2) + 16))/36

Trigonometric part [src]

         /         ___      \
  ___    |16 - 6*\/ 6  + 2*x|
\/ 6 *log|------------------|
         |               ___|
         \16 + 2*x + 6*\/ 6 /
-----------------------------
              36

$$\frac{\sqrt{6} \log{\left(\frac{2 x - 6 \sqrt{6} + 16}{2 x + 6 \sqrt{6} + 16} \right)}}{36}$$

sqrt(6)*log((16 - 6*sqrt(6) + 2*x)/(16 + 2*x + 6*sqrt(6)))/36

Common denominator [src]

         /                                            ___    \
  ___    |       8                 x              3*\/ 6     |
\/ 6 *log|--------------- + --------------- - ---------------|
         |            ___               ___               ___|
         \8 + x + 3*\/ 6    8 + x + 3*\/ 6    8 + x + 3*\/ 6 /
--------------------------------------------------------------
                              36

$$\frac{\sqrt{6} \log{\left(\frac{x}{x + 3 \sqrt{6} + 8} - \frac{3 \sqrt{6}}{x + 3 \sqrt{6} + 8} + \frac{8}{x + 3 \sqrt{6} + 8} \right)}}{36}$$

sqrt(6)*log(8/(8 + x + 3*sqrt(6)) + x/(8 + x + 3*sqrt(6)) - 3*sqrt(6)/(8 + x + 3*sqrt(6)))/36

Combining rational expressions [src]

         /            ___\
  ___    |8 + x - 3*\/ 6 |
\/ 6 *log|---------------|
         |            ___|
         \8 + x + 3*\/ 6 /
--------------------------
            36

$$\frac{\sqrt{6} \log{\left(\frac{x - 3 \sqrt{6} + 8}{x + 3 \sqrt{6} + 8} \right)}}{36}$$

sqrt(6)*log((8 + x - 3*sqrt(6))/(8 + x + 3*sqrt(6)))/36

Powers [src]

         /         ___      \
  ___    |16 - 6*\/ 6  + 2*x|
\/ 6 *log|------------------|
         |               ___|
         \16 + 2*x + 6*\/ 6 /
-----------------------------
              36

$$\frac{\sqrt{6} \log{\left(\frac{2 x - 6 \sqrt{6} + 16}{2 x + 6 \sqrt{6} + 16} \right)}}{36}$$

sqrt(6)*log((16 - 6*sqrt(6) + 2*x)/(16 + 2*x + 6*sqrt(6)))/36

Assemble expression [src]

         /       3/2     \
  ___    |2*x - 6    + 16|
\/ 6 *log|---------------|
         |       3/2     |
         \2*x + 6    + 16/
--------------------------
            36

$$\frac{\sqrt{6} \log{\left(\frac{\left(2 x - 6^{\frac{3}{2}}\right) + 16}{\left(2 x + 6^{\frac{3}{2}}\right) + 16} \right)}}{36}$$

sqrt(6)*log((2*x - 6^(3/2) + 16)/(2*x + 6^(3/2) + 16))/36

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Identical expressions

Similar expressions

Least common denominator log((2*x-6^(3/2)+16)/(2*x+6^(3/2)+16))/6^(3/2)

The solution

Least common denominator log((2x-6^(3/2)+16)/(2x+6^(3/2)+16))/6^(3/2)