Mister Exam

# Least common denominator (x/sqrt(x^2-8))-(7*x/(x^2-8+7*(sqrt(x^2-8))))

An expression to simplify:

### The solution

You have entered [src]
     x                 7*x
----------- - ----------------------
________                 ________
/  2         2           /  2
\/  x  - 8    x  - 8 + 7*\/  x  - 8 
$$\frac{x}{\sqrt{x^{2} - 8}} - \frac{7 x}{7 \sqrt{x^{2} - 8} + \left(x^{2} - 8\right)}$$
x/sqrt(x^2 - 8) - 7*x/(x^2 - 8 + 7*sqrt(x^2 - 8))
General simplification [src]
          _________
/       2
x*\/  -8 + x
------------------------
_________
2       /       2
-8 + x  + 7*\/  -8 + x  
$$\frac{x \sqrt{x^{2} - 8}}{x^{2} + 7 \sqrt{x^{2} - 8} - 8}$$
x*sqrt(-8 + x^2)/(-8 + x^2 + 7*sqrt(-8 + x^2))
Combinatorics [src]
          _________
/       2
x*\/  -8 + x
------------------------
_________
2       /       2
-8 + x  + 7*\/  -8 + x  
$$\frac{x \sqrt{x^{2} - 8}}{x^{2} + 7 \sqrt{x^{2} - 8} - 8}$$
x*sqrt(-8 + x^2)/(-8 + x^2 + 7*sqrt(-8 + x^2))
Combining rational expressions [src]
          _________
/       2
x*\/  -8 + x
------------------------
_________
2       /       2
-8 + x  + 7*\/  -8 + x  
$$\frac{x \sqrt{x^{2} - 8}}{x^{2} + 7 \sqrt{x^{2} - 8} - 8}$$
x*sqrt(-8 + x^2)/(-8 + x^2 + 7*sqrt(-8 + x^2))
Rational denominator [src]
                            _________           _________
5       3             3   /       2           /       2
x  - 16*x  + 64*x - 7*x *\/  -8 + x   + 56*x*\/  -8 + x
---------------------------------------------------------
_________
/       2  /       4       2\
\/  -8 + x  *\456 + x  - 65*x /             
$$\frac{x^{5} - 7 x^{3} \sqrt{x^{2} - 8} - 16 x^{3} + 56 x \sqrt{x^{2} - 8} + 64 x}{\sqrt{x^{2} - 8} \left(x^{4} - 65 x^{2} + 456\right)}$$
(x^5 - 16*x^3 + 64*x - 7*x^3*sqrt(-8 + x^2) + 56*x*sqrt(-8 + x^2))/(sqrt(-8 + x^2)*(456 + x^4 - 65*x^2))
Trigonometric part [src]
     x                   7*x
------------ - ------------------------
_________                  _________
/       2          2       /       2
\/  -8 + x     -8 + x  + 7*\/  -8 + x  
$$- \frac{7 x}{x^{2} + 7 \sqrt{x^{2} - 8} - 8} + \frac{x}{\sqrt{x^{2} - 8}}$$
x/sqrt(-8 + x^2) - 7*x/(-8 + x^2 + 7*sqrt(-8 + x^2))
0.353553390593274*x*(-1 + 0.125*x^2)^(-0.5) - 7.0*x/(-8.0 + x^2 + 19.7989898732233*(-1 + 0.125*x^2)^0.5)
0.353553390593274*x*(-1 + 0.125*x^2)^(-0.5) - 7.0*x/(-8.0 + x^2 + 19.7989898732233*(-1 + 0.125*x^2)^0.5)
Powers [src]
     x                   7*x
------------ - ------------------------
_________                  _________
/       2          2       /       2
\/  -8 + x     -8 + x  + 7*\/  -8 + x  
$$- \frac{7 x}{x^{2} + 7 \sqrt{x^{2} - 8} - 8} + \frac{x}{\sqrt{x^{2} - 8}}$$
x/sqrt(-8 + x^2) - 7*x/(-8 + x^2 + 7*sqrt(-8 + x^2))
Assemble expression [src]
     x                   7*x
------------ - ------------------------
_________                  _________
/       2          2       /       2
\/  -8 + x     -8 + x  + 7*\/  -8 + x  
$$- \frac{7 x}{x^{2} + 7 \sqrt{x^{2} - 8} - 8} + \frac{x}{\sqrt{x^{2} - 8}}$$
x/sqrt(-8 + x^2) - 7*x/(-8 + x^2 + 7*sqrt(-8 + x^2))
Common denominator [src]
       x
----------------
_________
/       2
7 + \/  -8 + x  
$$\frac{x}{\sqrt{x^{2} - 8} + 7}$$
x/(7 + sqrt(-8 + x^2))