Soalan 5:
Permudah setiap yang berikut.
$$ \text { (a) } \frac{m}{9}+\frac{n}{12} $$
$$ \text { (b) } \frac{3}{3 m n}+\frac{n}{6 m^2} $$
$$ \text { (c) } \frac{4}{d^2 g}+\frac{3}{5 d g} $$
Penyelesaian:
(a)
$$ \begin{aligned} \mathrm{GSTK} & =3 \times 3 \times 4 \\ & =36 \end{aligned} $$
$$ \begin{aligned} \frac{m}{9}+\frac{n}{12} & =\frac{m \times 4}{9 \times 4}+\frac{n \times 3}{12 \times 3} \\ & =\frac{4 m}{36}+\frac{3 n}{36} \\ & =\frac{4 m+3 n}{36} \end{aligned} $$
(b)
$$ \begin{aligned} \mathrm{GSTK} & =3 m \times n \times 2 m \\ & =6 m^2 n \end{aligned} $$
$$ \begin{aligned} & \frac{3}{3 m n}+\frac{n}{6 m^2} \\ & =\frac{3 \times 2 m}{3 m n \times 2 m}+\frac{n \times n}{6 m^2 \times n} \\ & =\frac{6 m}{6 m^2 n}+\frac{n^2}{6 m^2 n} \\ & =\frac{6 m+n^2}{6 m^2 n} \end{aligned} $$
(c)
$$ \begin{aligned} \text { GSTK } & =d g \times d \times 5 \\ & =5 d^2 g \end{aligned} $$
$$ \begin{aligned} \frac{4}{d^2 g}+\frac{3}{5 d g} & =\frac{4 \times 5}{d^2 g \times 5}+\frac{3 \times d}{5 d g \times d} \\ & =\frac{20}{5 d^2 g}+\frac{3 d}{5 d^2 g} \\ & =\frac{20+3 d}{5 d^2 g} \end{aligned} $$
Permudah setiap yang berikut.
$$ \text { (a) } \frac{m}{9}+\frac{n}{12} $$
$$ \text { (b) } \frac{3}{3 m n}+\frac{n}{6 m^2} $$
$$ \text { (c) } \frac{4}{d^2 g}+\frac{3}{5 d g} $$
Penyelesaian:
(a)
$$ \begin{aligned} \mathrm{GSTK} & =3 \times 3 \times 4 \\ & =36 \end{aligned} $$
$$ \begin{aligned} \frac{m}{9}+\frac{n}{12} & =\frac{m \times 4}{9 \times 4}+\frac{n \times 3}{12 \times 3} \\ & =\frac{4 m}{36}+\frac{3 n}{36} \\ & =\frac{4 m+3 n}{36} \end{aligned} $$
(b)
$$ \begin{aligned} \mathrm{GSTK} & =3 m \times n \times 2 m \\ & =6 m^2 n \end{aligned} $$
$$ \begin{aligned} & \frac{3}{3 m n}+\frac{n}{6 m^2} \\ & =\frac{3 \times 2 m}{3 m n \times 2 m}+\frac{n \times n}{6 m^2 \times n} \\ & =\frac{6 m}{6 m^2 n}+\frac{n^2}{6 m^2 n} \\ & =\frac{6 m+n^2}{6 m^2 n} \end{aligned} $$
(c)
$$ \begin{aligned} \text { GSTK } & =d g \times d \times 5 \\ & =5 d^2 g \end{aligned} $$
$$ \begin{aligned} \frac{4}{d^2 g}+\frac{3}{5 d g} & =\frac{4 \times 5}{d^2 g \times 5}+\frac{3 \times d}{5 d g \times d} \\ & =\frac{20}{5 d^2 g}+\frac{3 d}{5 d^2 g} \\ & =\frac{20+3 d}{5 d^2 g} \end{aligned} $$
Soalan 6:
Permudah.
$$ \text { (a) } \frac{x^2-x}{x y} $$
$$ \text { (b) } \frac{6 a+15}{12} $$
$$ \text { (c) } \frac{m+n}{m^2-n^2} $$
$$ \text { (d) } \frac{2 k-1}{4 k^2-1} $$
$$ \text { (e) } \frac{c^2-9}{2 c+6} $$
Penyelesaian:
(a)
$$ \begin{aligned} \frac{x^2-x}{x y} & =\frac{x(x-1)}{x y} \\ & =\frac{x-1}{y} \end{aligned} $$
(b)
$$ \begin{aligned} \frac{6 a+15}{12} & =\frac{3(2 a+5)}{12} \\ & =\frac{2 a+5}{4} \end{aligned} $$
(c)
$$ \begin{aligned} & \frac{m+n}{m^2-n^2} \\ = & \frac{m+n}{(m+n)(m-n)} \\ = & \frac{1}{m-n} \end{aligned} $$
(d)
$$ \begin{aligned} \frac{2 k-1}{4 k^2-1} & =\frac{2 k-1}{(2 k)^2-1^2} \\ & =\frac{2 k-1}{(2 k+1)(2 k-1)} \\ & =\frac{1}{2 k+1} \end{aligned} $$
(e)
$$ \begin{aligned} \frac{c^2-9}{2 c+6} & =\frac{c^2-3^2}{2(c+3)} \\ & =\frac{(\epsilon+3)(c-3)}{2(\epsilon+3)} \\ & =\frac{c-3}{2} \end{aligned} $$
Permudah.
$$ \text { (a) } \frac{x^2-x}{x y} $$
$$ \text { (b) } \frac{6 a+15}{12} $$
$$ \text { (c) } \frac{m+n}{m^2-n^2} $$
$$ \text { (d) } \frac{2 k-1}{4 k^2-1} $$
$$ \text { (e) } \frac{c^2-9}{2 c+6} $$
Penyelesaian:
(a)
$$ \begin{aligned} \frac{x^2-x}{x y} & =\frac{x(x-1)}{x y} \\ & =\frac{x-1}{y} \end{aligned} $$
(b)
$$ \begin{aligned} \frac{6 a+15}{12} & =\frac{3(2 a+5)}{12} \\ & =\frac{2 a+5}{4} \end{aligned} $$
(c)
$$ \begin{aligned} & \frac{m+n}{m^2-n^2} \\ = & \frac{m+n}{(m+n)(m-n)} \\ = & \frac{1}{m-n} \end{aligned} $$
(d)
$$ \begin{aligned} \frac{2 k-1}{4 k^2-1} & =\frac{2 k-1}{(2 k)^2-1^2} \\ & =\frac{2 k-1}{(2 k+1)(2 k-1)} \\ & =\frac{1}{2 k+1} \end{aligned} $$
(e)
$$ \begin{aligned} \frac{c^2-9}{2 c+6} & =\frac{c^2-3^2}{2(c+3)} \\ & =\frac{(\epsilon+3)(c-3)}{2(\epsilon+3)} \\ & =\frac{c-3}{2} \end{aligned} $$
Soalan 7:
Permudah.
$$ \text { (a) } \frac{2}{a-3} \times \frac{3}{3+a} $$
$$ \text { (b) } \frac{h}{k-2} \times \frac{y}{h+3} $$
$$ \text { (c) } \frac{3 m}{(m-n)} \times \frac{2 m n}{(n-2 m)} $$
$$ \text { (d) } \frac{2 r}{s-2} \times \frac{s-4}{r+5} $$
Penyelesaian:
(a)
$$ \frac{2}{a-3} \times \frac{3}{3+a}=\frac{6}{(a-3)(3+a)} $$
(b)
$$ \frac{h}{k-2} \times \frac{y}{h+3}=\frac{h y}{(k-2)(h+3)} $$
(c)
$$ \frac{3 m}{(m-n)} \times \frac{2 m n}{(n-2 m)}=\frac{6 m^2 n}{(m-n)(n-2 m)} $$
(d)
$$ \begin{aligned} \frac{2 r}{s-2} \times \frac{s-4}{r+5} & =\frac{2 r(s-4)}{(s-2)(r+5)} \\ & =\frac{2 r s-8 r}{r s+5 s-2 r-10} \end{aligned} $$
Permudah.
$$ \text { (a) } \frac{2}{a-3} \times \frac{3}{3+a} $$
$$ \text { (b) } \frac{h}{k-2} \times \frac{y}{h+3} $$
$$ \text { (c) } \frac{3 m}{(m-n)} \times \frac{2 m n}{(n-2 m)} $$
$$ \text { (d) } \frac{2 r}{s-2} \times \frac{s-4}{r+5} $$
Penyelesaian:
(a)
$$ \frac{2}{a-3} \times \frac{3}{3+a}=\frac{6}{(a-3)(3+a)} $$
(b)
$$ \frac{h}{k-2} \times \frac{y}{h+3}=\frac{h y}{(k-2)(h+3)} $$
(c)
$$ \frac{3 m}{(m-n)} \times \frac{2 m n}{(n-2 m)}=\frac{6 m^2 n}{(m-n)(n-2 m)} $$
(d)
$$ \begin{aligned} \frac{2 r}{s-2} \times \frac{s-4}{r+5} & =\frac{2 r(s-4)}{(s-2)(r+5)} \\ & =\frac{2 r s-8 r}{r s+5 s-2 r-10} \end{aligned} $$