Mister Exam

Lang:

Other calculators

How to use it?
Least common denominator:
y/x-(x*y-x^2)/(y-1)*(y-1)/x^2
(x-y/5*x-x+y)/y-x/8+8/5*x
((x/(y^2+x*y))+((x-y)/(x^2-x*y)))/((y^2)/(x^3-x*y))+(1/(x-y))
x/x+1/x/x^2
Factor polynomial:
z^3+3*z^2+3*z+3
z^2-z+5
z^2+8*z+41
z^2-2*z+10
Factor squared:
-y^4-7*y^2+9
y^4-8*y^2-6
y^4-4*y^2-3
y^4+8*y^2-6
How do you in partial fractions?:
((x+3)/(x^2+18*x+45))
(3*y^2-12)/(2*y^2-15*y+18)
1/(x^2+1)
((p^4)^8*p^10)/((p^7)^4*p^8)
How do you in partial fractions?:
log((6*x-2*sqrt(21))/(2*sqrt(21)+6*x))/(2*sqrt(21))
Identical expressions
log((six *x- two *sqrt(twenty-one))/(two *sqrt(twenty-one)+ six *x))/(two *sqrt(twenty-one))
logarithm of ((6 multiply by x minus 2 multiply by square root of (21)) divide by (2 multiply by square root of (21) plus 6 multiply by x)) divide by (2 multiply by square root of (21))
logarithm of ((six multiply by x minus two multiply by square root of (twenty minus one)) divide by (two multiply by square root of (twenty minus one) plus six multiply by x)) divide by (two multiply by square root of (twenty minus one))
log((6*x-2*√(21))/(2*√(21)+6*x))/(2*√(21))
log((6x-2sqrt(21))/(2sqrt(21)+6x))/(2sqrt(21))
log6x-2sqrt21/2sqrt21+6x/2sqrt21
log((6*x-2*sqrt(21)) divide by (2*sqrt(21)+6*x)) divide by (2*sqrt(21))
Similar expressions
log((6*x+2*sqrt(21))/(2*sqrt(21)+6*x))/(2*sqrt(21))
log((6*x-2*sqrt(21))/(2*sqrt(21)-6*x))/(2*sqrt(21))

Expression simplification/ Least common denominator/ log((6*x-2*sqrt(21))/(2*sqrt(21)+6*x))/(2*sqrt(21))

Least common denominator log((6x-2sqrt(21))/(2sqrt(21)+6x))/(2*sqrt(21))

The solution

You have entered [src]

   /          ____\
   |6*x - 2*\/ 21 |
log|--------------|
   |    ____      |
   \2*\/ 21  + 6*x/
-------------------
          ____     
      2*\/ 21

$$\frac{\log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{2 \sqrt{21}}$$

log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))/((2*sqrt(21)))

General simplification [src]

          /    ____      \
  ____    |- \/ 21  + 3*x|
\/ 21 *log|--------------|
          |   ____       |
          \ \/ 21  + 3*x /
--------------------------
            42

$$\frac{\sqrt{21} \log{\left(\frac{3 x - \sqrt{21}}{3 x + \sqrt{21}} \right)}}{42}$$

sqrt(21)*log((-sqrt(21) + 3*x)/(sqrt(21) + 3*x))/42

Fraction decomposition [src]

sqrt(21)*log(-2*sqrt(21)/(2*sqrt(21) + 6*x) + 6*x/(2*sqrt(21) + 6*x))/42

$$\frac{\sqrt{21} \log{\left(\frac{6 x}{6 x + 2 \sqrt{21}} - \frac{2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42}$$

          /         ____                    \
  ____    |     2*\/ 21            6*x      |
\/ 21 *log|- -------------- + --------------|
          |      ____             ____      |
          \  2*\/ 21  + 6*x   2*\/ 21  + 6*x/
---------------------------------------------
                      42

Rational denominator [src]

          /       2         ____\
  ____    |7 + 3*x  - 2*x*\/ 21 |
\/ 21 *log|---------------------|
          |              2      |
          \      -7 + 3*x       /
---------------------------------
                42

$$\frac{\sqrt{21} \log{\left(\frac{3 x^{2} - 2 \sqrt{21} x + 7}{3 x^{2} - 7} \right)}}{42}$$

sqrt(21)*log((7 + 3*x^2 - 2*x*sqrt(21))/(-7 + 3*x^2))/42

Numerical answer [src]

0.109108945117996*log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))

0.109108945117996*log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))

Powers [src]

          /      ____      \
  ____    |- 2*\/ 21  + 6*x|
\/ 21 *log|----------------|
          |     ____       |
          \ 2*\/ 21  + 6*x /
----------------------------
             42

$$\frac{\sqrt{21} \log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42}$$

sqrt(21)*log((-2*sqrt(21) + 6*x)/(2*sqrt(21) + 6*x))/42

Combining rational expressions [src]

          /    ____      \
  ____    |- \/ 21  + 3*x|
\/ 21 *log|--------------|
          |   ____       |
          \ \/ 21  + 3*x /
--------------------------
            42

$$\frac{\sqrt{21} \log{\left(\frac{3 x - \sqrt{21}}{3 x + \sqrt{21}} \right)}}{42}$$

sqrt(21)*log((-sqrt(21) + 3*x)/(sqrt(21) + 3*x))/42

Trigonometric part [src]

          /      ____      \
  ____    |- 2*\/ 21  + 6*x|
\/ 21 *log|----------------|
          |     ____       |
          \ 2*\/ 21  + 6*x /
----------------------------
             42

$$\frac{\sqrt{21} \log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42}$$

sqrt(21)*log((-2*sqrt(21) + 6*x)/(2*sqrt(21) + 6*x))/42

Common denominator [src]

          /       ____                  \
  ____    |     \/ 21           3*x     |
\/ 21 *log|- ------------ + ------------|
          |    ____           ____      |
          \  \/ 21  + 3*x   \/ 21  + 3*x/
-----------------------------------------
                    42

$$\frac{\sqrt{21} \log{\left(\frac{3 x}{3 x + \sqrt{21}} - \frac{\sqrt{21}}{3 x + \sqrt{21}} \right)}}{42}$$

sqrt(21)*log(-sqrt(21)/(sqrt(21) + 3*x) + 3*x/(sqrt(21) + 3*x))/42

Combinatorics [src]

          /         ____                    \
  ____    |     2*\/ 21            6*x      |
\/ 21 *log|- -------------- + --------------|
          |      ____             ____      |
          \  2*\/ 21  + 6*x   2*\/ 21  + 6*x/
---------------------------------------------
                      42

$$\frac{\sqrt{21} \log{\left(\frac{6 x}{6 x + 2 \sqrt{21}} - \frac{2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42}$$

sqrt(21)*log(-2*sqrt(21)/(2*sqrt(21) + 6*x) + 6*x/(2*sqrt(21) + 6*x))/42

Assemble expression [src]

          /          ____\
  ____    |6*x - 2*\/ 21 |
\/ 21 *log|--------------|
          |    ____      |
          \2*\/ 21  + 6*x/
--------------------------
            42

$$\frac{\sqrt{21} \log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42}$$

sqrt(21)*log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))/42

Expand expression [src]

          /          ____\
  ____    |6*x - 2*\/ 21 |
\/ 21 *log|--------------|
          |    ____      |
          \2*\/ 21  + 6*x/
--------------------------
            42

$$\frac{\sqrt{21} \log{\left(\frac{6 x - 2 \sqrt{21}}{6 x + 2 \sqrt{21}} \right)}}{42}$$

sqrt(21)*log((6*x - 2*sqrt(21))/(2*sqrt(21) + 6*x))/42

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator log((6*x-2*sqrt(21))/(2*sqrt(21)+6*x))/(2*sqrt(21))

The solution

Least common denominator log((6x-2sqrt(21))/(2sqrt(21)+6x))/(2*sqrt(21))