# Activities 5

### 5.1)

Calculate and simplify the expressions as much as possible:

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

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

### 5.2)

Calculate and simplify the expressions as much as possible:

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

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

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)
$\frac{-5h}{j}-\frac{hs}{k}$
b)
$\frac{jippi}{v}+\frac{hurra}{w}$
c)
$\frac{4}{x-y}+\frac{5}{z}$
d)
$\frac{i}{p}+\frac{q}{p+1}$
e)
$\frac{kl}{rl}-\frac{ky}{ry}$
f)
$\frac{a}{a-b}-\frac{b}{a+b}$
g)
$\frac{3}{2a}-\frac{5}{2a}+\frac{1}{2a}+\frac{7}{2a}$

a)
$\frac{-5h}{j}-\frac{hs}{k}$
b)
$\frac{jippi}{v}+\frac{hurra}{w}$
c)
$\frac{4}{x-y}+\frac{5}{z}$
d)
$\frac{i}{p}+\frac{q}{p+1}$
e)
$\frac{kl}{rl}-\frac{ky}{ry}$
f)
$\frac{a}{a-b}-\frac{b}{a+b}$
g)
$\frac{3}{2a}-\frac{5}{2a}+\frac{1}{2a}+\frac{7}{2a}$

### 5.4)

Simplify the expressions as much as possible:

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

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

You can find the solutions here.