Mister Exam

Lang:

Other calculators

How to use it?
Least common denominator:
tan(x^2)/(x*log(2))-x/(sqrt(x^2)*sqrt(1-x^2))+2*x*(1+tan(x^2)^2)*log(x)/log(2)
tan(x)^(2*(1-x)^(2/3))*(-4*log(tan(x))/(3*(1-x)^(1/3))+2*(1-x)^(2/3)*(1+tan(x)^2)/tan(x))
tan(x)^(1/x)*(-log(tan(x))/x^2+(1+tan(x)^2)/(x*tan(x)))
tan(pi)/9+tan(5*pi)/36/1-tan(5*pi)/36*tan(pi)/9
Factor polynomial:
y^2-4*y+4
x*y^3+x*y^2*b
x*y+2*x^2*y
x*y^2-16*x^3
Factor squared:
y^4-15*y^2+1
-y^4+12*y^2-11
-y^2+y*x+9*x^2
y^4-2*y^2+10
How do you in partial fractions?:
(x+3)/(x^2-1)
(x-3)/(x^2+1)
(x^2-x+1)/(x^2+x+1)
(x+1)/(x^3+x-2)
Identical expressions
sqrt(x^ two +a)/ two +x^ two /(two *sqrt(x^ two +a))+a*(one +x/sqrt(x^ two +a))/(two *(x+sqrt(x^ two +a)))
square root of (x squared plus a) divide by 2 plus x squared divide by (2 multiply by square root of (x squared plus a)) plus a multiply by (1 plus x divide by square root of (x squared plus a)) divide by (2 multiply by (x plus square root of (x squared plus a)))
square root of (x to the power of two plus a) divide by two plus x to the power of two divide by (two multiply by square root of (x to the power of two plus a)) plus a multiply by (one plus x divide by square root of (x to the power of two plus a)) divide by (two multiply by (x plus square root of (x to the power of two plus a)))
√(x^2+a)/2+x^2/(2*√(x^2+a))+a*(1+x/√(x^2+a))/(2*(x+√(x^2+a)))
sqrt(x2+a)/2+x2/(2*sqrt(x2+a))+a*(1+x/sqrt(x2+a))/(2*(x+sqrt(x2+a)))
sqrtx2+a/2+x2/2*sqrtx2+a+a*1+x/sqrtx2+a/2*x+sqrtx2+a
sqrt(x²+a)/2+x²/(2*sqrt(x²+a))+a*(1+x/sqrt(x²+a))/(2*(x+sqrt(x²+a)))
sqrt(x to the power of 2+a)/2+x to the power of 2/(2*sqrt(x to the power of 2+a))+a*(1+x/sqrt(x to the power of 2+a))/(2*(x+sqrt(x to the power of 2+a)))
sqrt(x^2+a)/2+x^2/(2sqrt(x^2+a))+a(1+x/sqrt(x^2+a))/(2(x+sqrt(x^2+a)))
sqrt(x2+a)/2+x2/(2sqrt(x2+a))+a(1+x/sqrt(x2+a))/(2(x+sqrt(x2+a)))
sqrtx2+a/2+x2/2sqrtx2+a+a1+x/sqrtx2+a/2x+sqrtx2+a
sqrtx^2+a/2+x^2/2sqrtx^2+a+a1+x/sqrtx^2+a/2x+sqrtx^2+a
sqrt(x^2+a) divide by 2+x^2 divide by (2*sqrt(x^2+a))+a*(1+x divide by sqrt(x^2+a)) divide by (2*(x+sqrt(x^2+a)))
Similar expressions
sqrt(x^2+a)/2+x^2/(2*sqrt(x^2+a))+a*(1+x/sqrt(x^2+a))/(2*(x-sqrt(x^2+a)))
sqrt(x^2+a)/2+x^2/(2*sqrt(x^2+a))+a*(1+x/sqrt(x^2-a))/(2*(x+sqrt(x^2+a)))
sqrt(x^2+a)/2+x^2/(2*sqrt(x^2+a))+a*(1+x/sqrt(x^2+a))/(2*(x+sqrt(x^2-a)))
sqrt(x^2+a)/2+x^2/(2*sqrt(x^2-a))+a*(1+x/sqrt(x^2+a))/(2*(x+sqrt(x^2+a)))
sqrt(x^2-a)/2+x^2/(2*sqrt(x^2+a))+a*(1+x/sqrt(x^2+a))/(2*(x+sqrt(x^2+a)))
sqrt(x^2+a)/2+x^2/(2*sqrt(x^2+a))+a*(1-x/sqrt(x^2+a))/(2*(x+sqrt(x^2+a)))
sqrt(x^2+a)/2-x^2/(2*sqrt(x^2+a))+a*(1+x/sqrt(x^2+a))/(2*(x+sqrt(x^2+a)))
sqrt(x^2+a)/2+x^2/(2*sqrt(x^2+a))-a*(1+x/sqrt(x^2+a))/(2*(x+sqrt(x^2+a)))

Expression simplification/ Least common denominator/ sqrt(x^2+a)/2+x^2/(2*sqrt(x^2+a))+a*(1+x/sqrt(x^2+a))/(2*(x+sqrt(x^2+a)))

Least common denominator sqrt(x^2+a)/2+x^2/(2sqrt(x^2+a))+a(1+x/sqrt(x^2+a))/(2*(x+sqrt(x^2+a)))

The solution

You have entered [src]

                                /         x     \
                              a*|1 + -----------|
   ________                     |       ________|
  /  2               2          |      /  2     |
\/  x  + a          x           \    \/  x  + a /
----------- + ------------- + -------------------
     2             ________     /       ________\
                  /  2          |      /  2     |
              2*\/  x  + a    2*\x + \/  x  + a /

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

sqrt(x^2 + a)/2 + x^2/((2*sqrt(x^2 + a))) + (a*(1 + x/sqrt(x^2 + a)))/((2*(x + sqrt(x^2 + a))))

General simplification [src]

   ________
  /      2 
\/  a + x

$$\sqrt{a + x^{2}}$$

sqrt(a + x^2)

Expand expression [src]

                                /         x     \
                              a*|1 + -----------|
   ________                     |       ________|
  /  2               2          |      /  2     |
\/  x  + a          x           \    \/  x  + a /
----------- + ------------- + -------------------
     2             ________     /       ________\
                  /  2          |      /  2     |
              2*\/  x  + a    2*\x + \/  x  + a /

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

sqrt(x^2 + a)/2 + x^2/(2*sqrt(x^2 + a)) + a*(1 + x/sqrt(x^2 + a))/(2*(x + sqrt(x^2 + a)))

Combining rational expressions [src]

   ________
  /      2 
\/  a + x

$$\sqrt{a + x^{2}}$$

sqrt(a + x^2)

Assemble expression [src]

                                /         x     \
                              a*|1 + -----------|
   ________                     |       ________|
  /      2           2          |      /      2 |
\/  a + x           x           \    \/  a + x  /
----------- + ------------- + -------------------
     2             ________              ________
                  /      2              /      2 
              2*\/  a + x     2*x + 2*\/  a + x

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

sqrt(a + x^2)/2 + x^2/(2*sqrt(a + x^2)) + a*(1 + x/sqrt(a + x^2))/(2*x + 2*sqrt(a + x^2))

Powers [src]

                                /         x     \
                              a*|1 + -----------|
   ________                     |       ________|
  /      2           2          |      /      2 |
\/  a + x           x           \    \/  a + x  /
----------- + ------------- + -------------------
     2             ________              ________
                  /      2              /      2 
              2*\/  a + x     2*x + 2*\/  a + x

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

sqrt(a + x^2)/2 + x^2/(2*sqrt(a + x^2)) + a*(1 + x/sqrt(a + x^2))/(2*x + 2*sqrt(a + x^2))

Rational denominator [src]

           ________                3/2                 3/2              ________
      4   /      2         /     2\          2 /     2\            2   /      2 
- 16*x *\/  a + x   + 16*a*\a + x /    + 16*x *\a + x /    - 16*a*x *\/  a + x  
--------------------------------------------------------------------------------
                                      /     2\                                  
                                 16*a*\a + x /

$$\frac{- 16 a x^{2} \sqrt{a + x^{2}} + 16 a \left(a + x^{2}\right)^{\frac{3}{2}} - 16 x^{4} \sqrt{a + x^{2}} + 16 x^{2} \left(a + x^{2}\right)^{\frac{3}{2}}}{16 a \left(a + x^{2}\right)}$$

(-16*x^4*sqrt(a + x^2) + 16*a*(a + x^2)^(3/2) + 16*x^2*(a + x^2)^(3/2) - 16*a*x^2*sqrt(a + x^2))/(16*a*(a + x^2))

Trigonometric part [src]

                                /         x     \
                              a*|1 + -----------|
   ________                     |       ________|
  /      2           2          |      /      2 |
\/  a + x           x           \    \/  a + x  /
----------- + ------------- + -------------------
     2             ________              ________
                  /      2              /      2 
              2*\/  a + x     2*x + 2*\/  a + x

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

sqrt(a + x^2)/2 + x^2/(2*sqrt(a + x^2)) + a*(1 + x/sqrt(a + x^2))/(2*x + 2*sqrt(a + x^2))

Numerical answer [src]

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

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

Common denominator [src]

           a       
x + ---------------
           ________
          /      2 
    x + \/  a + x

$$\frac{a}{x + \sqrt{a + x^{2}}} + x$$

x + a/(x + sqrt(a + x^2))

Combinatorics [src]

   ________
  /      2 
\/  a + x

$$\sqrt{a + x^{2}}$$

sqrt(a + x^2)

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator sqrt(x^2+a)/2+x^2/(2*sqrt(x^2+a))+a*(1+x/sqrt(x^2+a))/(2*(x+sqrt(x^2+a)))

The solution

Least common denominator sqrt(x^2+a)/2+x^2/(2sqrt(x^2+a))+a(1+x/sqrt(x^2+a))/(2*(x+sqrt(x^2+a)))