Mister Exam

# Least common denominator (a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))/(a-b)+(2*sqrt(b))/(sqrt(a)+sqrt(b))

An expression to simplify:

### The solution

You have entered [src]
/    ___       ___\
|a*\/ a  + b*\/ b |
|-----------------|
|    ___     ___  |          ___
\  \/ a  + \/ b   /      2*\/ b
------------------- + -------------
a - b            ___     ___
\/ a  + \/ b 
$$\frac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{\frac{1}{\sqrt{a} + \sqrt{b}} \left(\sqrt{a} a + \sqrt{b} b\right)}{a - b}$$
((a*sqrt(a) + b*sqrt(b))/(sqrt(a) + sqrt(b)))/(a - b) + (2*sqrt(b))/(sqrt(a) + sqrt(b))
General simplification [src]
 3/2    3/2       ___
a    + b    + 2*\/ b *(a - b)
-----------------------------
/  ___     ___\
(a - b)*\\/ a  + \/ b /   
$$\frac{a^{\frac{3}{2}} + b^{\frac{3}{2}} + 2 \sqrt{b} \left(a - b\right)}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)}$$
(a^(3/2) + b^(3/2) + 2*sqrt(b)*(a - b))/((a - b)*(sqrt(a) + sqrt(b)))
Common denominator [src]
         3/2    3/2         ___
b    - a    + 2*b*\/ a
2 + -------------------------------
3/2    3/2       ___       ___
a    - b    + a*\/ b  - b*\/ a 
$$\frac{- a^{\frac{3}{2}} + 2 \sqrt{a} b + b^{\frac{3}{2}}}{a^{\frac{3}{2}} - \sqrt{a} b + a \sqrt{b} - b^{\frac{3}{2}}} + 2$$
2 + (b^(3/2) - a^(3/2) + 2*b*sqrt(a))/(a^(3/2) - b^(3/2) + a*sqrt(b) - b*sqrt(a))
Assemble expression [src]
       ___             3/2    3/2
2*\/ b             a    + b
------------- + -----------------------
___     ___           /  ___     ___\
\/ a  + \/ b    (a - b)*\\/ a  + \/ b /
$$\frac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)}$$
2*sqrt(b)/(sqrt(a) + sqrt(b)) + (a^(3/2) + b^(3/2))/((a - b)*(sqrt(a) + sqrt(b)))
Rational denominator [src]
                  2                     2                             2                        2                               2
2 /  ___     ___\     2 /  ___     ___\      ___  3/2 /  ___     ___\          /  ___     ___\       3/2   ___ /  ___     ___\
a *\\/ a  - \/ b /  - b *\\/ a  - \/ b /  - \/ a *b   *\\/ a  - \/ b /  + 2*a*b*\\/ a  - \/ b /  + 3*a   *\/ b *\\/ a  - \/ b /
--------------------------------------------------------------------------------------------------------------------------------
3
(a - b)                                                             
$$\frac{3 a^{\frac{3}{2}} \sqrt{b} \left(\sqrt{a} - \sqrt{b}\right)^{2} - \sqrt{a} b^{\frac{3}{2}} \left(\sqrt{a} - \sqrt{b}\right)^{2} + a^{2} \left(\sqrt{a} - \sqrt{b}\right)^{2} + 2 a b \left(\sqrt{a} - \sqrt{b}\right)^{2} - b^{2} \left(\sqrt{a} - \sqrt{b}\right)^{2}}{\left(a - b\right)^{3}}$$
(a^2*(sqrt(a) - sqrt(b))^2 - b^2*(sqrt(a) - sqrt(b))^2 - sqrt(a)*b^(3/2)*(sqrt(a) - sqrt(b))^2 + 2*a*b*(sqrt(a) - sqrt(b))^2 + 3*a^(3/2)*sqrt(b)*(sqrt(a) - sqrt(b))^2)/(a - b)^3
Combining rational expressions [src]
 3/2    3/2       ___
a    + b    + 2*\/ b *(a - b)
-----------------------------
/  ___     ___\
(a - b)*\\/ a  + \/ b /   
$$\frac{a^{\frac{3}{2}} + b^{\frac{3}{2}} + 2 \sqrt{b} \left(a - b\right)}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)}$$
(a^(3/2) + b^(3/2) + 2*sqrt(b)*(a - b))/((a - b)*(sqrt(a) + sqrt(b)))
2.0*b^0.5/(a^0.5 + b^0.5) + (a^1.5 + b^1.5)/((a - b)*(a^0.5 + b^0.5))
2.0*b^0.5/(a^0.5 + b^0.5) + (a^1.5 + b^1.5)/((a - b)*(a^0.5 + b^0.5))
Combinatorics [src]
 3/2    3/2         ___
a    - b    + 2*a*\/ b
-----------------------
/  ___     ___\
(a - b)*\\/ a  + \/ b /
$$\frac{a^{\frac{3}{2}} + 2 a \sqrt{b} - b^{\frac{3}{2}}}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)}$$
(a^(3/2) - b^(3/2) + 2*a*sqrt(b))/((a - b)*(sqrt(a) + sqrt(b)))
Powers [src]
       ___             3/2    3/2
2*\/ b             a    + b
------------- + -----------------------
___     ___           /  ___     ___\
\/ a  + \/ b    (a - b)*\\/ a  + \/ b /
$$\frac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)}$$
2*sqrt(b)/(sqrt(a) + sqrt(b)) + (a^(3/2) + b^(3/2))/((a - b)*(sqrt(a) + sqrt(b)))
Trigonometric part [src]
       ___             3/2    3/2
2*\/ b             a    + b
------------- + -----------------------
___     ___           /  ___     ___\
\/ a  + \/ b    (a - b)*\\/ a  + \/ b /
$$\frac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{a^{\frac{3}{2}} + b^{\frac{3}{2}}}{\left(\sqrt{a} + \sqrt{b}\right) \left(a - b\right)}$$
2*sqrt(b)/(sqrt(a) + sqrt(b)) + (a^(3/2) + b^(3/2))/((a - b)*(sqrt(a) + sqrt(b)))