Bài giải:
Có: $\dfrac{a}{b}=\dfrac{c}{d}$
$\to \dfrac{b}{a}=\dfrac{d}{c}$
$\to 1+\dfrac{b}{a}=1+\dfrac{d}{c}$
$\to \dfrac{a+b}{a}=\dfrac{c+d}{c}(đpcm)$
Câu 2:
Có: $2^{450}=$ $ $($2^{3})^{150}=$ $8^{150}$
$3^{300}=$ $(3^{2})^{150}=$ $9^{150}$
Nhận thấy: $8^{150}<$ $9^{150}⇒$ $2^{450}<$ $3^{300}$
Vậy $2^{450}<$ $3^{300}$
Câu 3:
$\dfrac{x+2}{11}+$ $\dfrac{x+2}{12}+$ $\dfrac{x+2}{13}=$ $\dfrac{x+2}{14}+$ $\dfrac{x+2}{15}$
$⇒$ $\dfrac{x+2}{11}+$ $\dfrac{x+2}{12}+$ $\dfrac{x+2}{13}-$$\dfrac{x+2}{14}-$ $\dfrac{x+2}{15}=0$
$⇒$ $(x+2)(\dfrac{1}{11}+$ $\dfrac{1}{12}$+ $\dfrac{1}{13}$ - $\dfrac{1}{14}$ -$\dfrac{1}{15})=0$
$⇒$ $x + 2 = 0$ ( vì $\dfrac{1}{11}+$ $\dfrac{1}{12}$+ $\dfrac{1}{13}$ - $\dfrac{1}{14}$ -$\dfrac{1}{15}$ # 0)
$⇒$ $x = -2$
Vậy $x = -2$
