Mister Exam
Least common denominator (x/sqrt(x^2-8))-(7*x/(x^2-8+7*(sqrt(x^2-8))))
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))
Numerical answer
[src]
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))