a/ Cho ti le thuc \(\frac{a}{b}=\frac{c}{d}\)
Chung minh: \(\frac{2a+5b}{3a-7b}=\frac{2c+5d}{3c-7d}\)
b/ Cho ti le thuc: \(\frac{x}{y}=\frac{m}{n}\)
Chung minh; \(\frac{5x+4y}{3x-6y}=\frac{5m+4n}{3m-6n}\)
a/ Cho ti le thuc: \(\dfrac{a}{b}=\dfrac{c}{d}\)
Chung minh: \(\dfrac{2a+5b}{3a-7b}=\dfrac{2c+5d}{3c-7d}\)
b/ Cho ti le thuc: \(\dfrac{x}{y}=\dfrac{m}{n}\)
Chung minh: \(\dfrac{5x+4y}{3x-6y}=\dfrac{5m+4n}{3m-6n}\)
a) Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\) => a = kb ; c = dk
Ta có \(\dfrac{2a+5b}{3a-7b}=\dfrac{2bk+5b}{3bk-7b}=\dfrac{b\left(2k+5\right)}{b\left(3k-7\right)}=\dfrac{2k+5}{3k-7}\) (1)
\(\dfrac{2c+5d}{3c-7d}=\dfrac{2dk+5d}{3dk-7d}=\dfrac{d\left(2k+5\right)}{d\left(3k-7\right)}=\dfrac{2k+5}{3k-7}\) (2)
Từ (1) và (2) => \(\dfrac{2a+5b}{3a-7b}=\dfrac{2c+5d}{3c-7d}\)
cho ti le thuc \(\frac{a}{b}=\frac{c}{d}\)chung minh:
\(\frac{5a+2c}{5b+2d}=\frac{a-4c}{b-4d}\)
\(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{c}=\frac{b}{d}\)
Theo TCDTSBN:
\(\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}=\frac{a-b}{c-d}\Leftrightarrow\frac{a+b}{a-b}=\frac{c+d}{c-d}\left(đpcm\right)\)
Áp dụng TCDTSBN ta có:
\(\frac{a}{b}=\frac{c}{d}=\frac{5a}{5b}=\frac{2c}{2d}=\frac{4c}{4d}=\frac{5a+2c}{5b+2d}=\frac{a-4c}{b-4d}\)
k nhé!
Cho \(\frac{a}{b}=\frac{c}{d}\) Chung minh cac ti le thuc sau :
a) \(\frac{2a+c}{2b+d}=\frac{2a-c}{2b-d}\)
b) \(\frac{2a+3c}{a}=\frac{2b+3d}{b}\)
a.Ta có: \(\frac{a}{b}=\frac{2a}{2b}=\frac{c}{d}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\frac{a}{b}=\frac{2a}{2b}=\frac{c}{d}=\frac{2a+c}{2b+d}=\frac{2a-c}{2b-d}\)
cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\). Chứng minh
a)\(\frac{3a+5b}{3a-5b}=\frac{3c+5d}{3c-5d}\)
b)\(\frac{2a+3b}{2a-3b}=\frac{2c+3d}{2c-3d}\)
cho ti le thuc \(\frac{a}{b}\)=\(\frac{c}{d}\)
chung minh rang\(\frac{a}{b}\)=\(\frac{7a+5c}{7b+5d}\)[b+d khac 0]
cac ban co biet tai sao minh go dau cac chu cai thi chu cai do va dau deu bien mat khong? giup minh voi , cau hoi tren la 1 vi du
cho ti le thuc \(\frac{a}{b}=\frac{c}{d}\) chung minh rang \(\frac{a+b}{a-b}=\frac{c+d}{c-d}\)
a/b=c/d nên ad=bc
Ta có:
(a+b)(c-d)= ac -ad +bc -bd=ac-bd(1)
(a-b)(c+d)=ac+ad-bc-bd=ac-bd(2)
Từ (1) và (2) suy ra: (a+b)(c-d)=(a-b)(c+d) nên: (a+b)/(a-b)=(c+d)/(c-d)
A/D tỉ lệ thức ta dc :
\(\frac{a}{b}=\frac{c}{d}=>\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}=\frac{a-b}{c-d}\)
\(=>\frac{a+b}{c+d}=\frac{a-b}{c-d}=>\frac{a+b}{a-b}=\frac{c+d}{c-d}\)
đpcm
Gọi giá trị chung của các tỉ số đó là k, ta có :
\(\frac{a}{b}=\frac{c}{d}=k\)
\(\Rightarrow\) \(a=k\times b\) ; \(c=k\times d\)
Ta có :
\(\frac{a+b}{a-b}=\frac{k\times b+b}{k\times b-b}=\frac{b\times\left(k+1\right)}{b\times\left(k-1\right)}=\frac{k+1}{k-1}\) (1)
\(\frac{c+d}{c-d}=\frac{k\times d+d}{k\times d-d}=\frac{d\times\left(k+1\right)}{d\times\left(k-1\right)}=\frac{k+1}{k-1}\) (2)
Từ (1) và (2) \(\Rightarrow\) \(\frac{a+b}{a-b}=\frac{c+d}{c-d}\)
cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\).chứng minh
a)\(\frac{3a+5b}{3a-5b}=\frac{3c+5d}{3c-5d}\)
b) \(\frac{2a+3b}{2a-3b}\)=\(\frac{2c+3d}{2c-3d}\)
Cho \(\frac{a}{b}=\frac{c}{d}\)
\(\frac{a+b}{b}=\frac{c+d}{d}\)
\(\frac{a+c}{b+d}=\frac{a-c}{b-d}\)
\(\frac{3a+5b}{2a-7b}=\frac{3c+5d}{2c-7d}\)
Cho \(\frac{a}{b}=\frac{c}{d}\)Chứng minh \(\frac{3a+7b}{3a-5b}=\frac{3c+7d}{3c-5d}\)