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Least common denominator:
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b))/(a-b))^2
sqrt(sqrt(m)-sqrt((m^2-9)/m))*sqrt(sqrt(m)+sqrt((m^2-9)/m))
cos(a)/2*sin(2)-1-sin(a)/2*cos(2)-1
(x*(x-1)^2)^(1/3)*((x-1)^2/3+x*(-2+2*x)/3)/(x*(x-1)^2)
Factor polynomial:
x^6*y^9-64*x^3
x^6-x^8
49-m^2
x^7+x^5+1
Factor squared:
y^4+y^2+9
x^2-x*a+4*a^2
-y^4-y^2+8
-y^2-4*y-3
How do you in partial fractions?:
((y-9)/(y-8))*((y^2-64)/(y^2-16*y+64))
(e^(3x)+1)/(e^x+1)
y/(b*y-2*b^2)-2/(y^2+y-2*b*y-2*b)*(1+(3*y+y^2)/(3+y))
(u^2-4*u+16)/(16*u^2-1)*(4*u^2+u)/(u^3+64)
Identical expressions
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b))/(a-b))^ two
((a multiply by square root of (a) plus b multiply by square root of (b)) divide by ( square root of (a) plus square root of (b)) minus square root of (a multiply by b)) multiply by (( square root of (a) plus square root of (b)) divide by (a minus b)) squared
((a multiply by square root of (a) plus b multiply by square root of (b)) divide by ( square root of (a) plus square root of (b)) minus square root of (a multiply by b)) multiply by (( square root of (a) plus square root of (b)) divide by (a minus b)) to the power of two
((a*√(a)+b*√(b))/(√(a)+√(b))-√(a*b))*((√(a)+√(b))/(a-b))^2
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b))/(a-b))2
a*sqrta+b*sqrtb/sqrta+sqrtb-sqrta*b*sqrta+sqrtb/a-b2
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b))/(a-b))²
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b))/(a-b)) to the power of 2
((asqrt(a)+bsqrt(b))/(sqrt(a)+sqrt(b))-sqrt(ab))((sqrt(a)+sqrt(b))/(a-b))^2
((asqrt(a)+bsqrt(b))/(sqrt(a)+sqrt(b))-sqrt(ab))((sqrt(a)+sqrt(b))/(a-b))2
asqrta+bsqrtb/sqrta+sqrtb-sqrtabsqrta+sqrtb/a-b2
asqrta+bsqrtb/sqrta+sqrtb-sqrtabsqrta+sqrtb/a-b^2
((a*sqrt(a)+b*sqrt(b)) divide by (sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b)) divide by (a-b))^2
Similar expressions
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)-sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b))/(a-b))^2
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))+sqrt(a*b))*((sqrt(a)+sqrt(b))/(a-b))^2
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b))/(a+b))^2
((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)-sqrt(b))/(a-b))^2
((a*sqrt(a)-b*sqrt(b))/(sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b))/(a-b))^2

Expression simplification/ Least common denominator/ ((a*sqrt(a)+b*sqrt(b))/(sqrt(a)+sqrt(b))-sqrt(a*b))*((sqrt(a)+sqrt(b))/(a-b))^2

Least common denominator ((asqrt(a)+bsqrt(b))/(sqrt(a)+sqrt(b))-sqrt(ab))((sqrt(a)+sqrt(b))/(a-b))^2

The solution

You have entered [src]

                                             2
/    ___       ___          \ /  ___     ___\ 
|a*\/ a  + b*\/ b      _____| |\/ a  + \/ b | 
|----------------- - \/ a*b |*|-------------| 
|    ___     ___            | \    a - b    / 
\  \/ a  + \/ b             /

$$\left(\frac{\sqrt{a} + \sqrt{b}}{a - b}\right)^{2} \left(- \sqrt{a b} + \frac{\sqrt{a} a + \sqrt{b} b}{\sqrt{a} + \sqrt{b}}\right)$$

((a*sqrt(a) + b*sqrt(b))/(sqrt(a) + sqrt(b)) - sqrt(a*b))*((sqrt(a) + sqrt(b))/(a - b))^2

General simplification [src]

/  ___     ___\ / 3/2    3/2     _____ /  ___     ___\\
\\/ a  + \/ b /*\a    + b    - \/ a*b *\\/ a  + \/ b //
-------------------------------------------------------
                               2                       
                        (a - b)

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

(sqrt(a) + sqrt(b))*(a^(3/2) + b^(3/2) - sqrt(a*b)*(sqrt(a) + sqrt(b)))/(a - b)^2

Assemble expression [src]

               2 /              3/2    3/2 \
/  ___     ___\  |    _____    a    + b    |
\\/ a  + \/ b / *|- \/ a*b  + -------------|
                 |              ___     ___|
                 \            \/ a  + \/ b /
--------------------------------------------
                         2                  
                  (a - b)

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

(sqrt(a) + sqrt(b))^2*(-sqrt(a*b) + (a^(3/2) + b^(3/2))/(sqrt(a) + sqrt(b)))/(a - b)^2

Numerical answer [src]

(a^0.5 + b^0.5)^2*(-(a*b)^0.5 + (a^1.5 + b^1.5)/(a^0.5 + b^0.5))/(a - b)^2

(a^0.5 + b^0.5)^2*(-(a*b)^0.5 + (a^1.5 + b^1.5)/(a^0.5 + b^0.5))/(a - b)^2

Rational denominator [src]

/  ___     ___\ / 3/2    3/2     _____ /  ___     ___\\
\\/ a  + \/ b /*\a    + b    - \/ a*b *\\/ a  + \/ b //
-------------------------------------------------------
                               2                       
                        (a - b)

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

(sqrt(a) + sqrt(b))*(a^(3/2) + b^(3/2) - sqrt(a*b)*(sqrt(a) + sqrt(b)))/(a - b)^2

Combinatorics [src]

               2                                
/  ___     ___\  /          _____     ___   ___\
\\/ a  + \/ b / *\a + b - \/ a*b  - \/ a *\/ b /
------------------------------------------------
                           2                    
                    (a - b)

$$\frac{\left(\sqrt{a} + \sqrt{b}\right)^{2} \left(- \sqrt{a} \sqrt{b} + a + b - \sqrt{a b}\right)}{\left(a - b\right)^{2}}$$

(sqrt(a) + sqrt(b))^2*(a + b - sqrt(a*b) - sqrt(a)*sqrt(b))/(a - b)^2

Trigonometric part [src]

               2 /              3/2    3/2 \
/  ___     ___\  |    _____    a    + b    |
\\/ a  + \/ b / *|- \/ a*b  + -------------|
                 |              ___     ___|
                 \            \/ a  + \/ b /
--------------------------------------------
                         2                  
                  (a - b)

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

(sqrt(a) + sqrt(b))^2*(-sqrt(a*b) + (a^(3/2) + b^(3/2))/(sqrt(a) + sqrt(b)))/(a - b)^2

Expand expression [src]

               2 /    ___       ___              \
/  ___     ___\  |a*\/ a  + b*\/ b      ___   ___|
\\/ a  + \/ b / *|----------------- - \/ a *\/ b |
                 |    ___     ___                |
                 \  \/ a  + \/ b                 /
--------------------------------------------------
                            2                     
                     (a - b)

$$\frac{\left(\sqrt{a} + \sqrt{b}\right)^{2} \left(- \sqrt{a} \sqrt{b} + \frac{\sqrt{a} a + \sqrt{b} b}{\sqrt{a} + \sqrt{b}}\right)}{\left(a - b\right)^{2}}$$

               2 /    ___       ___          \
/  ___     ___\  |a*\/ a  + b*\/ b      _____|
\\/ a  + \/ b / *|----------------- - \/ a*b |
                 |    ___     ___            |
                 \  \/ a  + \/ b             /
----------------------------------------------
                          2                   
                   (a - b)

$$\frac{\left(\sqrt{a} + \sqrt{b}\right)^{2} \left(- \sqrt{a b} + \frac{\sqrt{a} a + \sqrt{b} b}{\sqrt{a} + \sqrt{b}}\right)}{\left(a - b\right)^{2}}$$

(sqrt(a) + sqrt(b))^2*((a*sqrt(a) + b*sqrt(b))/(sqrt(a) + sqrt(b)) - sqrt(a*b))/(a - b)^2

Powers [src]

               2 /              3/2    3/2 \
/  ___     ___\  |    _____    a    + b    |
\\/ a  + \/ b / *|- \/ a*b  + -------------|
                 |              ___     ___|
                 \            \/ a  + \/ b /
--------------------------------------------
                         2                  
                  (a - b)

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

(sqrt(a) + sqrt(b))^2*(-sqrt(a*b) + (a^(3/2) + b^(3/2))/(sqrt(a) + sqrt(b)))/(a - b)^2

Common denominator [src]

     5/2    5/2    3/2   _____    3/2   _____        3/2        3/2         ___   _____         ___   _____
    a    + b    + a   *\/ a*b  + b   *\/ a*b  - 5*a*b    - 5*b*a    + 3*a*\/ b *\/ a*b  + 3*b*\/ a *\/ a*b 
2 - -------------------------------------------------------------------------------------------------------
                             5/2    5/2     ___  2    2   ___        3/2        3/2                        
                            a    + b    + \/ a *b  + a *\/ b  - 2*a*b    - 2*b*a

$$2 - \frac{a^{\frac{5}{2}} - 5 a^{\frac{3}{2}} b + a^{\frac{3}{2}} \sqrt{a b} + 3 \sqrt{a} b \sqrt{a b} - 5 a b^{\frac{3}{2}} + 3 a \sqrt{b} \sqrt{a b} + b^{\frac{5}{2}} + b^{\frac{3}{2}} \sqrt{a b}}{a^{\frac{5}{2}} - 2 a^{\frac{3}{2}} b + \sqrt{a} b^{2} + a^{2} \sqrt{b} - 2 a b^{\frac{3}{2}} + b^{\frac{5}{2}}}$$

2 - (a^(5/2) + b^(5/2) + a^(3/2)*sqrt(a*b) + b^(3/2)*sqrt(a*b) - 5*a*b^(3/2) - 5*b*a^(3/2) + 3*a*sqrt(b)*sqrt(a*b) + 3*b*sqrt(a)*sqrt(a*b))/(a^(5/2) + b^(5/2) + sqrt(a)*b^2 + a^2*sqrt(b) - 2*a*b^(3/2) - 2*b*a^(3/2))

Combining rational expressions [src]

/  ___     ___\ / 3/2    3/2     _____ /  ___     ___\\
\\/ a  + \/ b /*\a    + b    - \/ a*b *\\/ a  + \/ b //
-------------------------------------------------------
                               2                       
                        (a - b)

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

(sqrt(a) + sqrt(b))*(a^(3/2) + b^(3/2) - sqrt(a*b)*(sqrt(a) + sqrt(b)))/(a - b)^2

Other calculators

How to use it?

Identical expressions

Similar expressions

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

The solution

Least common denominator ((asqrt(a)+bsqrt(b))/(sqrt(a)+sqrt(b))-sqrt(ab))((sqrt(a)+sqrt(b))/(a-b))^2