Mister Exam
Least common denominator z/4*(x-y)-2*z/x-y
The solution
You have entered
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z 2*z -*(x - y) - --- - y 4 x
$$- y + \left(\frac{z}{4} \left(x - y\right) - \frac{2 z}{x}\right)$$
(z/4)*(x - y) - 2*z/x - y
General simplification
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-8*z + x*(-4*y + z*(x - y))
---------------------------
4*x
$$\frac{x \left(- 4 y + z \left(x - y\right)\right) - 8 z}{4 x}$$
(-8*z + x*(-4*y + z*(x - y)))/(4*x)
Rational denominator
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-8*z - 4*x*y + x*z*(x - y)
--------------------------
4*x
$$\frac{- 4 x y + x z \left(x - y\right) - 8 z}{4 x}$$
(-8*z - 4*x*y + x*z*(x - y))/(4*x)
Trigonometric part
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2*z z*(x - y)
-y - --- + ---------
x 4
$$- y + \frac{z \left(x - y\right)}{4} - \frac{2 z}{x}$$
-y - 2*z/x + z*(x - y)/4
Assemble expression
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/ y x\ 2*z
-y + z*|- - + -| - ---
\ 4 4/ x
$$- y + z \left(\frac{x}{4} - \frac{y}{4}\right) - \frac{2 z}{x}$$
/ 2 y x\
-y + z*|- - - - + -|
\ x 4 4/
$$- y + z \left(\frac{x}{4} - \frac{y}{4} - \frac{2}{x}\right)$$
2*z z*(x - y)
-y - --- + ---------
x 4
$$- y + \frac{z \left(x - y\right)}{4} - \frac{2 z}{x}$$
-y - 2*z/x + z*(x - y)/4
Common denominator
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2*z y*z x*z
-y - --- - --- + ---
x 4 4
$$\frac{x z}{4} - \frac{y z}{4} - y - \frac{2 z}{x}$$
-y - 2*z/x - y*z/4 + x*z/4
Combinatorics
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2
-8*z + z*x - 4*x*y - x*y*z
---------------------------
4*x
$$\frac{x^{2} z - x y z - 4 x y - 8 z}{4 x}$$
(-8*z + z*x^2 - 4*x*y - x*y*z)/(4*x)
Combining rational expressions
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z*(-8 + x*(x - y)) - 4*x*y
--------------------------
4*x
$$\frac{- 4 x y + z \left(x \left(x - y\right) - 8\right)}{4 x}$$
(z*(-8 + x*(x - y)) - 4*x*y)/(4*x)
Powers
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2*z z*(x - y)
-y - --- + ---------
x 4
$$- y + \frac{z \left(x - y\right)}{4} - \frac{2 z}{x}$$
-y - 2*z/x + z*(x - y)/4