These aren't equations, just expressions you have to evaluate.
In order to add two fractions that have different denominators, you need to express those fractions in terms of a common denominator by finding the LCM of all the denominators involved.
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For the first expression,
[tex]\mathrm{lcm}(22,15)=330[/tex]
because 22 = 2 * 11 and 15 = 3 * 5 share no common divisors, so the LCM would be their product.
Mixed fractions should be rewritten as improper ones:
[tex]1\dfrac{11}{15}=\dfrac{15}{15}+\dfrac{11}{15}=\dfrac{15+11}{15}=\dfrac{26}{15}[/tex]
Now rewrite everything in terms of the common denominator:
[tex]\dfrac{21}{22}=\dfrac{21\cdot15}{22\cdot15}=\dfrac{315}{330}[/tex]
[tex]\dfrac4{15}=\dfrac{4\cdot22}{15\cdot22}=\dfrac{88}{330}[/tex]
[tex]\dfrac{26}{15}=\dfrac{26\cdot22}{15\cdot22}=\dfrac{572}{330}[/tex]
[tex]\implies\left(\dfrac{21}{22}+\dfrac4{15}\right)+1\dfrac{11}{15}=\dfrac{315}{330}+\dfrac{88}{330}+\dfrac{572}{330}=\dfrac{975}{330}[/tex]
and we can rewrite this as a mixed fraction, noting that 975 = 2 * 330 + 315:
[tex]\dfrac{975}{330}=\dfrac{2\cdot330+315}{330}=2\dfrac{315}{330}=2\dfrac{21}{22}[/tex]
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For the second expression,
[tex]\mathrm{lcm}(14,32)=224[/tex]
because 14 * 32 = 448, but 14 = 2 * 7 and 32 = 2^5 already share one common factor of 2 that we can factor out from 448.
Then
[tex]\dfrac3{14}=\dfrac{3\cdot16}{14\cdot16}=\dfrac{48}{224}[/tex]
[tex]\dfrac9{32}=\dfrac{9\cdot7}{32\cdot7}=\dfrac{63}{224}[/tex]
[tex]\implies\dfrac3{14}+\dfrac9{32}=\dfrac{48+63}{224}=\dfrac{111}{224}[/tex]
Dividing by a fraction is the same as multiply by the reciprocal of the fraction by which you're dividing. In other words,
[tex]\dfrac{111}{224}\div\dfrac3{56}=\dfrac{111}{224}\cdot\dfrac{56}3=\dfrac{111\cdot56}{224\cdot3}=\dfrac{6216}{672}[/tex]
Noticing that 6216 = 9 * 672 + 168, we end up with
[tex]\dfrac{6216}{672}=9\dfrac{168}{672}=9\dfrac14[/tex]
