Mister Exam
Least common denominator (49*b/a-25*a/b)/(7*a+5*b)
The solution
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49*b 25*a ---- - ---- a b ----------- 7*a + 5*b
$$\frac{- \frac{25 a}{b} + \frac{49 b}{a}}{7 a + 5 b}$$
((49*b)/a - 25*a/b)/(7*a + 5*b)
General simplification
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2 2 - 25*a + 49*b --------------- a*b*(5*b + 7*a)
$$\frac{- 25 a^{2} + 49 b^{2}}{a b \left(7 a + 5 b\right)}$$
(-25*a^2 + 49*b^2)/(a*b*(5*b + 7*a))
Common denominator
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/ 2 2\
-\- 49*b + 25*a /
-------------------
2 2
5*a*b + 7*b*a
$$- \frac{25 a^{2} - 49 b^{2}}{7 a^{2} b + 5 a b^{2}}$$
-(-49*b^2 + 25*a^2)/(5*a*b^2 + 7*b*a^2)
Combining rational expressions
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2 2 - 25*a + 49*b --------------- a*b*(5*b + 7*a)
$$\frac{- 25 a^{2} + 49 b^{2}}{a b \left(7 a + 5 b\right)}$$
(-25*a^2 + 49*b^2)/(a*b*(5*b + 7*a))
Combinatorics
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-(-7*b + 5*a)*(5*a + 7*b)
--------------------------
a*b*(5*b + 7*a)
$$- \frac{\left(5 a - 7 b\right) \left(5 a + 7 b\right)}{a b \left(7 a + 5 b\right)}$$
-(-7*b + 5*a)*(5*a + 7*b)/(a*b*(5*b + 7*a))
Rational denominator
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2 2 - 25*a + 49*b --------------- a*b*(5*b + 7*a)
$$\frac{- 25 a^{2} + 49 b^{2}}{a b \left(7 a + 5 b\right)}$$
(-25*a^2 + 49*b^2)/(a*b*(5*b + 7*a))