Question

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Answer 1

6.36

1)

$\frac{1}{4x} + \frac{1}{2y} = \frac{y}{4xy} + \frac{2x}{4xy} = \frac{y + 2x}{4xy}$

2)

$\frac{5}{3a} - \frac{2}{9b} = \frac{15b}{9ab} - \frac{2a}{9ab} = \frac{15b - 2a}{9ab}$

3)

$\frac{a}{6m} + \frac{b}{8n} = \frac{4an}{24mn} + \frac{3bm}{24mn} = \frac{4an + 3bm}{24mn}$

4)

$\frac{x}{12a} - \frac{y}{18b} = \frac{3bx}{36ab} - \frac{2ay}{36ab} = \frac{3bx - 2ay}{36ab}$

6.37

1)

$\frac{x}{ab} + \frac{x}{ac} = \frac{xc}{abc} + \frac{xb}{abc} = \frac{xc + xb}{abc}$

2)

$\frac{a}{xy} - \frac{b}{xz} = \frac{az}{xyz} - \frac{by}{xyz} = \frac{az - by}{xyz}$

3)

$\frac{2m}{ax} + \frac{3n}{bx} = \frac{2bm}{abx} + \frac{3an}{abx} = \frac{2bm + 3an}{abx}$

4)

$\frac{5a}{mn} - \frac{3b}{mp} = \frac{5ap}{mnp} - \frac{3bn}{mnp} = \frac{5ap - 3bn}{mnp}$

6.38

1)

$\frac{2x - 3y}{x} + \frac{4 {x}^{2} - 5 {y}^{2} }{xy} = \frac{2xy - 3 {y}^{2} }{xy} + \frac{4 {x}^{2} - 5 {y}^{2} }{xy} = \frac{2xy - 3 {y}^{2} + 4 {x}^{2} - 5 {y}^{2} }{xy} = \frac{4 {x}^{2} + 2xy - 8 {y}^{2} }{xy}$

2)

$\frac{5 {a}^{2} - {b}^{2} }{ab} - \frac{3a - 2b}{b} = \frac{5 {a}^{2} - {b}^{2} }{ab} - \frac{3 {a}^{2} - 2ab }{ab} = \frac{5 {a}^{2} - {b}^{2} - 3 {a}^{2} + 2ab }{ab} = \frac{2 {a}^{2} + 2ab - {b}^{2} }{ab}$

3)

$\frac{2 {b}^{2} + 3ax }{bx} - \frac{ab + 5bx}{ax} = \frac{2a {b}^{2} + 3 {a}^{2} x}{abx} - \frac{a {b}^{2} + 5 {b}^{2} x}{abx} = \frac{2a {b}^{2} + 3 {a}^{2} x - a {b}^{2} - 5 {b}^{2} x}{abx} = \frac{a {b}^{2} + 3 {a}^{2} x - 5 {b}^{2} x}{abx}$

4)

$\frac{3 {p}^{2} + 5mn}{mp} + \frac{ {n}^{2} - 3mp }{np} = \frac{3 n{p}^{2} + 5m {n}^{2} }{mnp} + \frac{m {n}^{2} - 3 {m}^{2} p }{mnp} = \frac{3n {p}^{2} + 5m {n}^{2} + m {n}^{2} - 3 {m}^{2} p}{mnp} = \\ \\ = \frac{3n {p}^{2} + 6m {n}^{2} - 3 {m}^{2} p }{mnp}$