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*a) ------------ 2 2 a - b
$$\frac{a \left(2 a - b\right)}{a^{2} - b^{2}}$$
a*(-b + 2*a)/(a^2 - b^2)
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))
Common denominator
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2
- 2*b + a*b
2 - ------------
2 2
a - b
$$2 - \frac{a b - 2 b^{2}}{a^{2} - b^{2}}$$
2 - (-2*b^2 + a*b)/(a^2 - b^2)
Combinatorics
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a*(-b + 2*a) --------------- (a + b)*(a - b)
$$\frac{a \left(2 a - b\right)}{\left(a - b\right) \left(a + b\right)}$$
a*(-b + 2*a)/((a + b)*(a - b))
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))