Mister Exam
Least common denominator exp((y+z)^2)/(x+w)-exp(y^2)/x
The solution
You have entered
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/ 2\ / 2\ \(y + z) / \y / e e ----------- - ----- x + w x
$$\frac{e^{\left(y + z\right)^{2}}}{w + x} - \frac{e^{y^{2}}}{x}$$
exp((y + z)^2)/(x + w) - exp(y^2)/x
General simplification
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/ 2\ / 2\
\(y + z) / \y /
x*e - (w + x)*e
-----------------------------
x*(w + x)
$$\frac{x e^{\left(y + z\right)^{2}} - \left(w + x\right) e^{y^{2}}}{x \left(w + x\right)}$$
(x*exp((y + z)^2) - (w + x)*exp(y^2))/(x*(w + x))
Rational denominator
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/ 2\ / 2\
\(y + z) / \y /
x*e - (w + x)*e
-----------------------------
x*(w + x)
$$\frac{x e^{\left(y + z\right)^{2}} - \left(w + x\right) e^{y^{2}}}{x \left(w + x\right)}$$
(x*exp((y + z)^2) - (w + x)*exp(y^2))/(x*(w + x))
Combinatorics
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/ / 2\ \ / 2\
| \z / 2*y*z| \y /
\-w - x + x*e *e /*e
-------------------------------
x*(w + x)
$$\frac{\left(- w + x e^{z^{2}} e^{2 y z} - x\right) e^{y^{2}}}{x \left(w + x\right)}$$
(-w - x + x*exp(z^2)*exp(2*y*z))*exp(y^2)/(x*(w + x))
Combining rational expressions
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/ 2\ / 2\
\(y + z) / \y /
x*e - (w + x)*e
-----------------------------
x*(w + x)
$$\frac{x e^{\left(y + z\right)^{2}} - \left(w + x\right) e^{y^{2}}}{x \left(w + x\right)}$$
(x*exp((y + z)^2) - (w + x)*exp(y^2))/(x*(w + x))
Common denominator
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/ 2\ / 2\ / 2\ / 2\
\y / \y / \y / \z / 2*y*z
- w*e - x*e + x*e *e *e
------------------------------------------
2
x + w*x
$$\frac{- w e^{y^{2}} + x e^{y^{2}} e^{z^{2}} e^{2 y z} - x e^{y^{2}}}{w x + x^{2}}$$
(-w*exp(y^2) - x*exp(y^2) + x*exp(y^2)*exp(z^2)*exp(2*y*z))/(x^2 + w*x)
Trigonometric part
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/ 2\ / 2\ / 2\ / 2\
cosh\(y + z) / + sinh\(y + z) / cosh\y / + sinh\y /
------------------------------- - -------------------
w + x x
$$\frac{\sinh{\left(\left(y + z\right)^{2} \right)} + \cosh{\left(\left(y + z\right)^{2} \right)}}{w + x} - \frac{\sinh{\left(y^{2} \right)} + \cosh{\left(y^{2} \right)}}{x}$$
(cosh((y + z)^2) + sinh((y + z)^2))/(w + x) - (cosh(y^2) + sinh(y^2))/x