Mister Exam
Least common denominator (y/5*x-5*x-y)/(y+5*x)
The solution
You have entered
[src]
y -*x - 5*x - y 5 ------------- y + 5*x
$$\frac{- y + \left(x \frac{y}{5} - 5 x\right)}{5 x + y}$$
((y/5)*x - 5*x - y)/(y + 5*x)
General simplification
[src]
x*y
-y - 5*x + ---
5
--------------
y + 5*x
$$\frac{\frac{x y}{5} - 5 x - y}{5 x + y}$$
(-y - 5*x + x*y/5)/(y + 5*x)
Rational denominator
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-25*x - 5*y + x*y
-----------------
5*y + 25*x
$$\frac{x y - 25 x - 5 y}{25 x + 5 y}$$
(-25*x - 5*y + x*y)/(5*y + 25*x)
Common denominator
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2
y y
-1 + -- - ------------
25 25*y + 125*x
$$- \frac{y^{2}}{125 x + 25 y} + \frac{y}{25} - 1$$
-1 + y/25 - y^2/(25*y + 125*x)
Assemble expression
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/ x\
-5*x + y*|-1 + -|
\ 5/
-----------------
y + 5*x
$$\frac{- 5 x + y \left(\frac{x}{5} - 1\right)}{5 x + y}$$
/ y\
-y + x*|-5 + -|
\ 5/
---------------
y + 5*x
$$\frac{x \left(\frac{y}{5} - 5\right) - y}{5 x + y}$$
x*y
-y - 5*x + ---
5
--------------
y + 5*x
$$\frac{\frac{x y}{5} - 5 x - y}{5 x + y}$$
(-y - 5*x + x*y/5)/(y + 5*x)
Trigonometric part
[src]
x*y
-y - 5*x + ---
5
--------------
y + 5*x
$$\frac{\frac{x y}{5} - 5 x - y}{5 x + y}$$
(-y - 5*x + x*y/5)/(y + 5*x)
Combinatorics
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-25*x - 5*y + x*y ----------------- 5*(y + 5*x)
$$\frac{x y - 25 x - 5 y}{5 \left(5 x + y\right)}$$
(-25*x - 5*y + x*y)/(5*(y + 5*x))
Powers
[src]
x*y
-y - 5*x + ---
5
--------------
y + 5*x
$$\frac{\frac{x y}{5} - 5 x - y}{5 x + y}$$
(-y - 5*x + x*y/5)/(y + 5*x)
Combining rational expressions
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-5*y + x*(-25 + y) ------------------ 5*(y + 5*x)
$$\frac{x \left(y - 25\right) - 5 y}{5 \left(5 x + y\right)}$$
(-5*y + x*(-25 + y))/(5*(y + 5*x))