Cho tỉ lệ thức [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex] . Chứng minh: a) [tex]\frac{a+b}{b}= \frac{c+d}{d}[/tex] b) [tex]\frac{a}{a+b} = \frac{c}{d+c} c) \frac{a-b}{a} = \frac{c-d}{c}[/tex] d) [tex]\frac{a}{a-b} = \frac{c}{c-d} e) \frac{a+b}{a-b} = \frac{c+d}{c-d} f) \frac{3a-2c}{3a-2d} = \frac{a+3cc}{d+3d} g) \frac{5a+3b}{5a-3b} = \frac{5c+3d}{5c-3d}[/tex] Cảm ơn :>
Lười đặt quá nên làm thế này =))) [tex] \frac{a}{b}=\frac{c}{d}\Rightarrow \frac{b}{a}=\frac{d}{c}; \frac{a}{c}=\frac{b}{d}[/tex] a) [tex]\frac{a}{b}=\frac{c}{d}\Rightarrow \frac{a}{b}+1=\frac{c}{d}+1 \Leftrightarrow \frac{a+b}{b}=\frac{c+d}{d}[/tex] b) [tex]\frac{a}{a+b}=\frac{1}{\frac{a+b}{a}}=\frac{1}{1+\frac{b}{a}}[/tex] [tex]\frac{c}{c+d}=\frac{1}{\frac{c+d}{c}}=\frac{1}{1+\frac{d}{c}}[/tex] Vì [tex]\frac{b}{a}=\frac{d}{c} \Rightarrow \frac{a}{a+b}=\frac{c}{c+d}[/tex] c) [tex]\frac{b}{a}= \frac{d}{c} \Rightarrow 1-\frac{b}{a} = 1-\frac{d}{c} \Leftrightarrow \frac{a-b}{a}=\frac{c-d}{c} [/tex] d) Nghịch đảo câu c) e)[tex]\frac{a+b}{a-b}=\frac{2a}{a-b}-1;\frac{c+d}{c-d}=\frac{2c}{c-d}-1[/tex] Vì [tex]\frac{a}{a-b}=\frac{c}{c-d} \Rightarrow \frac{a+b}{a-b}=\frac{c+d}{c-d}[/tex] f) Có vấn đề... g) [tex]\frac{a}{c}=\frac{b}{d}\Rightarrow \frac{5a}{5c}=\frac{3b}{3d}= \frac{5a+3b}{5c+3d}=\frac{5a-3b}{5c-3d}[/tex] (Dãy tỉ số bằng nhau) [TEX]\Rightarrow \frac{5a+3b}{5a-3b} = \frac{5c+3d}{5c-3d}[/TEX]
