Mister Exam
Least common denominator a/(a+b)+a^2/(b^2-a^2)
The solution
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2
a a
----- + -------
a + b 2 2
b - a
$$\frac{a^{2}}{- a^{2} + b^{2}} + \frac{a}{a + b}$$
a/(a + b) + a^2/(b^2 - a^2)
General simplification
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-a*b ------- 2 2 a - b
$$- \frac{a b}{a^{2} - b^{2}}$$
-a*b/(a^2 - b^2)
Rational denominator
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/ 2 2\ 2
a*\b - a / + a *(a + b)
------------------------
/ 2 2\
(a + b)*\b - a /
$$\frac{a^{2} \left(a + b\right) + a \left(- a^{2} + b^{2}\right)}{\left(a + b\right) \left(- a^{2} + b^{2}\right)}$$
(a*(b^2 - a^2) + a^2*(a + b))/((a + b)*(b^2 - a^2))
Combinatorics
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-a*b --------------- (a + b)*(a - b)
$$- \frac{a b}{\left(a - b\right) \left(a + b\right)}$$
-a*b/((a + b)*(a - b))
Combining rational expressions
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/ 2 2 \
a*\b - a + a*(a + b)/
-----------------------
/ 2 2\
(a + b)*\b - a /
$$\frac{a \left(- a^{2} + a \left(a + b\right) + b^{2}\right)}{\left(a + b\right) \left(- a^{2} + b^{2}\right)}$$
a*(b^2 - a^2 + a*(a + b))/((a + b)*(b^2 - a^2))