Question

Express in simplest form. Show steps solve parts a and b​

Answer 1

$\tt{(a) \ {\dfrac{5(p - q)}{2}} - {\dfrac{2q - p}{14}} - {\dfrac{2(p + q)}{7}}}$

$\tt{\implies {\dfrac{7[5(p - q)] - 1(2q - p) - 2[2(p + q)]}{14}}}$

$\tt{\implies {\dfrac{35(p - q) - (2q - p) - 4(p + q)}{14}}}$

$\tt{\implies {\dfrac{35p - 35q - 2q + p - 4p - 4q}{14}}}$

$\tt\red{\implies {\dfrac{32p - 41q}{14}}}$



$\tt{(b) - {\dfrac{2a + b}{3}} - {\dfrac{3(a - 3b)}{2}} - {\dfrac{4(a + 2b)}{5}}}$

$\tt{\implies {\dfrac{- 10(2a + b) - 15[3(a - 3b)] - 6[4(a + 2b)]}{30}}}$

$\tt{\implies {\dfrac{- 10(2a + b) - 45(a - 3b) - 24(a + 2b)}{30}}}$

$\tt{\implies {\dfrac{- 20a - 20b - 45a + 135b - 24a - 48b}{30}}}$

$\tt\red{\implies {\dfrac{68b - 89a}{20}}}$