1.Tính bằng 2 cách:
a,\(\left(\frac{5}{7}+\frac{9}{7}\right)x\frac{21}{28}\) b,\(\frac{4}{5}x\frac{13}{14}+\frac{13}{14}x\frac{1}{5}\)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
A) \(\frac{7}{\left(x+3\right)\left(x+10\right)}+\frac{11}{\left(x+10\right)\left(x+21\right)}+\frac{13}{\left(x+21\right)\left(x+34\right)}\)
\(=\frac{\left(x+10\right)-\left(x+3\right)}{\left(x+3\right)\left(x+10\right)}+\frac{\left(x+21\right)-\left(x+10\right)}{\left(x+10\right)\left(x+21\right)}+\frac{\left(x+34\right)-\left(x+21\right)}{\left(x+21\right)\left(x+34\right)}\)
\(=\frac{1}{x+3}-\frac{1}{x+10}+\frac{1}{x+10}-\frac{1}{x+21}+\frac{1}{x+21}-\frac{1}{x+34}\)
\(=\frac{1}{x+3}-\frac{1}{x+34}\)
\(=\frac{\left(x+34\right)-\left(x+3\right)}{\left(x+3\right)\left(x+34\right)}\)\(=\frac{x}{\left(x+3\right)\left(x+34\right)}\)
\(\Rightarrow\left(x+34\right)-\left(x+3\right)=x\)
\(\Rightarrow x=31\)
Vậy, x = 31
Bạn áp dụng: \(\frac{k}{x\cdot\left(x+k\right)}=\frac{1}{x}-\frac{1}{x+k}\) với \(x,k\inℝ;x\ne0;x\ne-k\)
Chứng minh: \(\frac{1}{x}-\frac{1}{x+k}=\frac{x+k}{x\left(x+k\right)}-\frac{x}{x\left(x+k\right)}=\frac{x+k-x}{x\left(x+k\right)}=\frac{k}{x\left(x+k\right)}\)
\(a,\left(\frac{5}{7}+\frac{9}{7}\right)x\frac{21}{28}\)
\(C1:=\frac{14}{7}x\frac{21}{28}=\frac{3}{2}\)
\(C2:=\frac{5}{7}x\frac{21}{28}+\frac{9}{7}x\frac{21}{28}=\frac{15}{28}+\frac{27}{28}=\frac{3}{2}\)
\(b,\frac{4}{5}x\frac{13}{14}+\frac{13}{14}x\frac{1}{5}\)
\(C1:=\frac{26}{35}+\frac{13}{70}=\frac{13}{14}\)
\(C2:=\frac{13}{14}x\left(\frac{4}{5}+\frac{1}{5}\right)=\frac{13}{14}x1=\frac{13}{14}\)
học tốt ~~~
Cảm ơn bạn!