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