Mister Exam
Least common denominator x^2*y+16/(y-1)*(x-4)-16*y+x^2/x*y-x-4*y+4
The solution
You have entered
[src]
2
2 16 x
x *y + -----*(x - 4) - 16*y + --*y - x - 4*y + 4
y - 1 x
$$\left(- 4 y + \left(- x + \left(y \frac{x^{2}}{x} + \left(- 16 y + \left(x^{2} y + \left(x - 4\right) \frac{16}{y - 1}\right)\right)\right)\right)\right) + 4$$
x^2*y + (16/(y - 1))*(x - 4) - 16*y + (x^2/x)*y - x - 4*y + 4
General simplification
[src]
/ 2\
-64 + 16*x + (-1 + y)*\4 - x - 20*y + x*y + y*x /
-------------------------------------------------
-1 + y
$$\frac{16 x + \left(y - 1\right) \left(x^{2} y + x y - x - 20 y + 4\right) - 64}{y - 1}$$
(-64 + 16*x + (-1 + y)*(4 - x - 20*y + x*y + y*x^2))/(-1 + y)
Rational denominator
[src]
/ 2 \ 2 2
x*\-64 + 16*x - 16*y*(-1 + y) + y*x *(-1 + y)/ - x *(-1 + y) + 4*x*(-1 + y) + y*x *(-1 + y) - 4*x*y*(-1 + y)
------------------------------------------------------------------------------------------------------------
x*(-1 + y)
$$\frac{x^{2} y \left(y - 1\right) - x^{2} \left(y - 1\right) - 4 x y \left(y - 1\right) + 4 x \left(y - 1\right) + x \left(x^{2} y \left(y - 1\right) + 16 x - 16 y \left(y - 1\right) - 64\right)}{x \left(y - 1\right)}$$
(x*(-64 + 16*x - 16*y*(-1 + y) + y*x^2*(-1 + y)) - x^2*(-1 + y) + 4*x*(-1 + y) + y*x^2*(-1 + y) - 4*x*y*(-1 + y))/(x*(-1 + y))
Assemble expression
[src]
/ 2\ 16*(-4 + x)
4 - x + y*\-20 + x + x / + -----------
-1 + y
$$- x + y \left(x^{2} + x - 20\right) + \frac{16 \left(x - 4\right)}{y - 1} + 4$$
2 16*(-4 + x)
4 - x - 20*y + x*y + y*x + -----------
-1 + y
$$x^{2} y + x y - x - 20 y + \frac{16 \left(x - 4\right)}{y - 1} + 4$$
2 16*(-4 + x)
4 - 20*y + x*(-1 + y) + y*x + -----------
-1 + y
$$x^{2} y + x \left(y - 1\right) - 20 y + \frac{16 \left(x - 4\right)}{y - 1} + 4$$
4 - 20*y + x*(-1 + y) + y*x^2 + 16*(-4 + x)/(-1 + y)
Powers
[src]
2 -64 + 16*x
4 - x - 20*y + x*y + y*x + ----------
-1 + y
$$x^{2} y + x y - x - 20 y + \frac{16 x - 64}{y - 1} + 4$$
2 16*(-4 + x)
4 - x - 20*y + x*y + y*x + -----------
-1 + y
$$x^{2} y + x y - x - 20 y + \frac{16 \left(x - 4\right)}{y - 1} + 4$$
4 - x - 20*y + x*y + y*x^2 + 16*(-4 + x)/(-1 + y)
Combining rational expressions
[src]
2
-68 + 4*y + 16*x - x*(-1 + y) - 20*y*(-1 + y) + x*y*(-1 + y) + y*x *(-1 + y)
----------------------------------------------------------------------------
-1 + y
$$\frac{x^{2} y \left(y - 1\right) + x y \left(y - 1\right) - x \left(y - 1\right) + 16 x - 20 y \left(y - 1\right) + 4 y - 68}{y - 1}$$
(-68 + 4*y + 16*x - x*(-1 + y) - 20*y*(-1 + y) + x*y*(-1 + y) + y*x^2*(-1 + y))/(-1 + y)
Numerical answer
[src]
4.0 - x - 20.0*y + x*y + y*x^2 + 16.0*(-4.0 + x)/(-1.0 + y)
4.0 - x - 20.0*y + x*y + y*x^2 + 16.0*(-4.0 + x)/(-1.0 + y)
Combinatorics
[src]
/ 2 2 \
(-4 + x)*\17 - 6*y + 5*y + x*y - x*y/
---------------------------------------
-1 + y
$$\frac{\left(x - 4\right) \left(x y^{2} - x y + 5 y^{2} - 6 y + 17\right)}{y - 1}$$
(-4 + x)*(17 - 6*y + 5*y^2 + x*y^2 - x*y)/(-1 + y)
Common denominator
[src]
2 -64 + 16*x
4 - x - 20*y + x*y + y*x + ----------
-1 + y
$$x^{2} y + x y - x - 20 y + \frac{16 x - 64}{y - 1} + 4$$
4 - x - 20*y + x*y + y*x^2 + (-64 + 16*x)/(-1 + y)
Trigonometric part
[src]
2 16*(-4 + x)
4 - x - 20*y + x*y + y*x + -----------
-1 + y
$$x^{2} y + x y - x - 20 y + \frac{16 \left(x - 4\right)}{y - 1} + 4$$
4 - x - 20*y + x*y + y*x^2 + 16*(-4 + x)/(-1 + y)