giúp mik bài3B 4A vs ạ
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\(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\)
a)\(\frac{a-b}{a+b}=\frac{c-d}{c+d}\)
\(\Leftrightarrow\left(a-b\right)\left(c+d\right)=\left(c-d\right)\left(a+b\right)\)
\(\Leftrightarrow ac-bc+ad-bd=ac-ad+bc-bd\)
\(\text{Thay }ad=bc\text{ vào}\Rightarrow ac-ad+ad-bd=ac-ad+ad-bd\)
\(\text{Đây là đẳng thức đúng }\Rightarrow\frac{a-b}{a+b}=\frac{c-d}{c+d}\text{ là đúng }\)
b)\(\text{Tương tự*}\)
a) \(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{a}{b}+1=\frac{c}{d}+1\Leftrightarrow\frac{a+b}{b}=\frac{c+d}{d}\Leftrightarrow\frac{b}{a+b}=\frac{d}{c+d}\)
\(\Leftrightarrow\frac{-2b}{a+b}+1=\frac{-2d}{c+d}+1\Leftrightarrow\frac{a-b}{a+b}=\frac{c-d}{c+d}\)
b) \(\frac{a}{b}=\frac{c}{d}\Leftrightarrow\frac{4a}{b}-5=\frac{4c}{d}-5\Leftrightarrow\frac{4a-5b}{b}=\frac{4c-5d}{d}\Leftrightarrow\frac{b}{4a-5b}=\frac{d}{4c-5d}\)
\(\Leftrightarrow\frac{11b}{4a-5b}+1=\frac{11d}{4c-5d}+1\Leftrightarrow\frac{4a+6b}{4a-5b}=\frac{4c+6d}{4c-5d}\Leftrightarrow\frac{2a+3b}{4a-5b}=\frac{2c+3d}{4c-5d}\)
\(\Leftrightarrow\frac{2a+3b}{2c+3d}=\frac{4a-5b}{4c-5d}\)
e: \(E=\dfrac{x^2-9-x^2+4-x^2+9}{\left(x+3\right)\left(x-2\right)}\)
\(=\dfrac{x+2}{x+3}\)
a: \(A=\dfrac{4x^2+x^2-2x+1+x^2+2x+1}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{6x^2+2}{\left(x-1\right)\left(x+1\right)}\)
27. unforgetable
câu 31 đổi thành ...if I can give him his guide....
câu 32 thiếu on trong turned on và đổi thành has been turned on vì câu gốc là HTHT
câu 33 rút gọn mệnh đề ok
câu 34 hơi phân vân nhưng mình thấy đúng
3B.
a.
\(\dfrac{6}{7-x}+\dfrac{-4}{x}+\dfrac{6}{x-7}+\dfrac{2}{x-2}+\dfrac{4}{x}+\dfrac{-5}{x+2}\)
\(=\dfrac{6}{7-x}-\dfrac{6}{7-x}+\dfrac{-4+4}{x}+\dfrac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{-5\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=0+0+\dfrac{2x+4-5x+10}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{-3x+14}{\left(x-2\right)\left(x+2\right)}\)
b.
\(\dfrac{x-1}{x^2-4}-\dfrac{1}{x+2}+\dfrac{x+2}{x}+\dfrac{1}{x+2}+\dfrac{x+2}{-x}-\dfrac{3}{x-2}\)
\(=\dfrac{x-1}{\left(x-2\right)\left(x+2\right)}-\dfrac{3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\left(\dfrac{1}{x+2}-\dfrac{1}{x+2}\right)+\left(\dfrac{x+2}{x}-\dfrac{x+2}{x}\right)\)
\(=\dfrac{x-1-3x-6}{\left(x-2\right)\left(x+2\right)}+0+0\)
\(=\dfrac{-2x-7}{\left(x-2\right)\left(x+2\right)}\)
4A.
\(\dfrac{3x+1}{\left(x-1\right)^2}-\dfrac{1}{x+1}+\dfrac{x+3}{1-x^2}\)
\(=\dfrac{\left(3x+1\right)\left(x+1\right)}{\left(x+1\right)\left(x-1\right)^2}-\dfrac{\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)^2}-\dfrac{\left(x+3\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)^2}\)
\(=\dfrac{3x^2+4x+1-\left(x^2-2x+1\right)-\left(x^2+2x-3\right)}{\left(x+1\right)\left(x-1\right)^2}\)
\(=\dfrac{x^2+4x+3}{\left(x+1\right)\left(x-1\right)^2}=\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x+1\right)\left(x-1\right)^2}\)
\(=\dfrac{x+3}{\left(x-1\right)^2}\)
b.
\(\dfrac{2x}{x^2-4}-\left(\dfrac{2}{x+5}+\dfrac{3-x}{x+1}\right)+\left(\dfrac{2}{x+5}-\left(\dfrac{4}{x^2-4}+\dfrac{x-3}{x+1}\right)\right)\)
\(=\dfrac{2x}{x^2-4}+\left(\dfrac{2}{x+5}-\dfrac{2}{x+5}\right)+\left(\dfrac{x-3}{x+1}-\dfrac{x-3}{x+1}\right)-\dfrac{4}{x^2-4}\)
\(=\dfrac{2x-4}{x^2-4}=\dfrac{2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{2}{x+2}\)