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Activities 5

5.1)

Calculate and simplify the expressions as much as possible:

a): $\frac{3 x y}{x}$
b): $\frac{12 x^{2} y}{4 y}$
c): $\frac{a^{3}}{a b}$
d): $\frac{a}{a^{3} b^{2}}$
e): $\frac{a^{2} + a^{3}}{a b}$
f): $\frac{2 a^{2} + 1}{2 a^{2}}$
g): $\frac{2 a + 4 a^{2}}{8 a^{2} + 2 a}$
h): $\frac{2 x + 4 x^{2}}{6 x^{2} + 1}$
i): $\frac{6 x y + 2 x}{3 y + 6 x y}$
j): $\frac{4 x}{3 x + 3 y} + \frac{6 x y + 2 x}{3 y + 3 x}$

a): $\frac{3 x y}{x}$
b): $\frac{12 x^{2} y}{4 y}$
c): $\frac{a^{3}}{a b}$
d): $\frac{a}{a^{3} b^{2}}$
e): $\frac{a^{2} + a^{3}}{a b}$
f): $\frac{2 a^{2} + 1}{2 a^{2}}$
g): $\frac{2 a + 4 a^{2}}{8 a^{2} + 2 a}$
h): $\frac{2 x + 4 x^{2}}{6 x^{2} + 1}$
i): $\frac{6 x y + 2 x}{3 y + 6 x y}$
j): $\frac{4 x}{3 x + 3 y} + \frac{6 x y + 2 x}{3 y + 3 x}$

5.2)

Calculate and simplify the expressions as much as possible:

a): $\frac{3}{x} + \frac{4 y}{x y}$
b): $\frac{2}{5} - \frac{3 x}{10 x}$
c): $\frac{4}{k} + \frac{4}{r}$
d): $\frac{13 b}{4 a} + \frac{7 a}{2 b}$
e): $\frac{10 u^{2}}{3 u} - \frac{4 u}{3}$
f): $\frac{12 l}{7 p} - \frac{8 l}{14 p}$
g): $\frac{88}{25 g} - \frac{8}{5 g}$
h): $\frac{a p}{4 p} + \frac{7 a}{3}$

a): $\frac{3}{x} + \frac{4 y}{x y}$
b): $\frac{2}{5} - \frac{3 x}{10 x}$
c): $\frac{4}{k} + \frac{4}{r}$
d): $\frac{13 b}{4 a} + \frac{7 a}{2 b}$
e): $\frac{10 u^{2}}{3 u} - \frac{4 u}{3}$
f): $\frac{12 l}{7 p} - \frac{8 l}{14 p}$
g): $\frac{88}{25 g} - \frac{8}{5 g}$
h): $\frac{a p}{4 p} + \frac{7 a}{3}$

Hint: Sometimes it can be smart to simplify first.

5.3)

Write the expressions as a single fraction and simplify as much as possible:

a): $\frac{- 5 h}{j} - \frac{h s}{k}$
b): $\frac{j i p p i}{v} + \frac{h u r r a}{w}$
c): $\frac{4}{x - y} + \frac{5}{z}$
d): $\frac{i}{p} + \frac{q}{p + 1}$
e): $\frac{k l}{r l} - \frac{k y}{r y}$
f): $\frac{a}{a - b} - \frac{b}{a + b}$
g): $\frac{3}{2 a} - \frac{5}{2 a} + \frac{1}{2 a} + \frac{7}{2 a}$

a): $\frac{- 5 h}{j} - \frac{h s}{k}$
b): $\frac{j i p p i}{v} + \frac{h u r r a}{w}$
c): $\frac{4}{x - y} + \frac{5}{z}$
d): $\frac{i}{p} + \frac{q}{p + 1}$
e): $\frac{k l}{r l} - \frac{k y}{r y}$
f): $\frac{a}{a - b} - \frac{b}{a + b}$
g): $\frac{3}{2 a} - \frac{5}{2 a} + \frac{1}{2 a} + \frac{7}{2 a}$

5.4)

Simplify the expressions as much as possible:

a): $\frac{2 b}{a + 1}$
b): $\frac{4 b a}{8 a + 2 b}$
c): $\frac{3 b}{a + b} + \frac{4 a}{2 a + 2 b}$
d): $\frac{11}{a + 2} + \frac{a + 2}{4 (a + 2)}$
e): $\frac{32}{a + 4} - \frac{a}{8}$
f): $\frac{5}{a} + \frac{a + 1}{a}$
g): $\frac{32}{x} + \frac{y + 1}{x} - \frac{23 y}{x} + \frac{4 y}{y}$
h): $\frac{2}{x} + \frac{y + 2}{x} - \frac{15 y}{x} + \frac{4}{y}$

a): $\frac{2 b}{a + 1}$
b): $\frac{4 b a}{8 a + 2 b}$
c): $\frac{3 b}{a + b} + \frac{4 a}{2 a + 2 b}$
d): $\frac{11}{a + 2} + \frac{a + 2}{4 (a + 2)}$
e): $\frac{32}{a + 4} - \frac{a}{8}$
f): $\frac{5}{a} + \frac{a + 1}{a}$
g): $\frac{32}{x} + \frac{y + 1}{x} - \frac{23 y}{x} + \frac{4 y}{y}$
h): $\frac{2}{x} + \frac{y + 2}{x} - \frac{15 y}{x} + \frac{4}{y}$

You can find the solutions here.

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