Bài 1: Cho abc = 1 .Tính A= \(\dfrac{a}{ab+a+1}\)+\(\dfrac{b}{bc+b+1}\)+\(\dfrac{c}{ca+c+1}\).
Bài 2: Cho x-y=7 . Tính giá trị biểu thức B= \(\dfrac{3x-7}{2x+y}\)-\(\dfrac{3y+7}{2y+x}\).
Bài 3: Cho a+b+c=2018 và \(\dfrac{1}{a+b}\)+\(\dfrac{1}{b+c}\)+\(\dfrac{1}{c+a}\)=\(\dfrac{1}{2}\). Tính S=\(\dfrac{a}{b+c}\)+\(\dfrac{b}{c+a}\)+\(\dfrac{c}{a+b}\).
Bài 4: Cho 3 số a,b,c khác nhau và khác 0 thỏa mãn điều kiện \(\dfrac{a}{b+c}\)=\(\dfrac{b}{a+c}\)=\(\dfrac{c}{a+b}\)
Tính giá trị biểu thức P=\(\dfrac{b+c}{a}\)+\(\dfrac{a+c}{b}\)+\(\dfrac{a+b}{c}\).
Bài 5: Cho tỉ lệ \(\dfrac{3x-y}{x+y}\)=\(\dfrac{3}{4}\). Tính giá trị tỉ số \(\dfrac{x}{y}\).
Câu 2 :
\(x-y=7\)
\(\Rightarrow x=7+y\)
*)
\(B=\dfrac{3\left(7+y\right)-7}{2\left(7+y\right)+y}-\dfrac{3y+7}{2y+7+y}\)
\(=\dfrac{21+3y-7}{14+3y}-\dfrac{3y+7}{3y+7}\)
\(=\dfrac{14y+3y}{14y+3y}-1\)
\(=1-1\)
\(=0\)
Vậy B = 0
2/ Ta có :
\(B=\dfrac{3x-7}{2x+y}-\dfrac{3y+7}{2y+x}\)
\(=\dfrac{3x-\left(x-y\right)}{2x+y}-\dfrac{3y+\left(x-y\right)}{2y+x}\)
\(=\dfrac{3x-x+y}{2y+x}-\dfrac{3y+x-y}{2y+x}\)
\(=\dfrac{2x+y}{2x+y}-\dfrac{2y+x}{2y+x}\)
\(=1-1=0\)
Bài 3:
\(a+b+c=2018\text{ và }\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{c+a}\)
\(2018\left(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{c+a}\right)=\dfrac{1}{2}.2018\)
\(\Rightarrow\dfrac{2018}{a+b}+\dfrac{2018}{b+c}+\dfrac{2018}{a+c}=1009\)
\(\Rightarrow\dfrac{\left(a+b\right)+c}{a+b}+\dfrac{a+\left(b+c\right)}{b+c}+\dfrac{b+\left(a+c\right)}{a+c}=1009\)
\(\Rightarrow1+\dfrac{c}{a+b}+\dfrac{a}{b+c}+1+\dfrac{b}{a+c}+1=1009\)
\(\Rightarrow\dfrac{a}{b+c}+\dfrac{b}{a+c}+\dfrac{c}{a+b}=1009-3\)
\(\Rightarrow S=1006\)
Vậy \(S=1006\)
Nhiều qá, lm từng câu 1 nhé bn!
1/ \(A=\dfrac{a}{ab+a+1}+\dfrac{b}{bc+b+1}+\dfrac{c}{ca+c+1}\)
\(=\dfrac{abc}{ab+a+abc}+\dfrac{b}{bc+b+1}+\dfrac{1}{1+bc+b}\)
\(=\dfrac{abc}{a\left(b+1+bc\right)}+\dfrac{b+1}{bc+b+1}\)
\(=\dfrac{bc}{b+1+bc}+\dfrac{b+1}{bc+b+1}\)
\(=\dfrac{bc+b+1}{bc+b+1}\)
\(=1\)
Bài 5:
Có \(\dfrac{3x-y}{x+y}=\dfrac{3}{4}\)
=> 4(3x-y)=3(x+y)
=>12x-4y=3x+3y
=>12x-3x=3y+4y
=>9x=7y
=>\(\dfrac{x}{y}=\dfrac{7}{9}\)
