已知a/b=3/2,求a/a+b + b/a-b的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/14 15:01:03
已知a/b=3/2,求a/a+b + b/a-b的值
xTN0~\MLd%{jhikhQ$gL@^vNi(wgc;rwZK(#\#"Osꡈvqk+֪8D haA+>w[_DP~(@[9d^CԽB 0VA.]@34nfnT|JAe0Vf =lVaoY9"K8 -3TJ1CU7(_N*ADq$,@끓Y" ƌH0"e¬_Z&d95AJup g؁pÝ D]抓}Uhr2lޘ^G|0+9JKnQ+TVU+:qJ_ ԴxD%?UuZ`aCRӘV(mL?52

已知a/b=3/2,求a/a+b + b/a-b的值
已知a/b=3/2,求a/a+b + b/a-b的值

已知a/b=3/2,求a/a+b + b/a-b的值
原式=(a²-ab)/(a+b)(a-b)+(ab+b²)/(a+b)(a-b)→化成同分母
=(a²-ab+ab+b²)/(a²-b²)→同分母运算(因式分解→平方差公式)
=(a²+b²)/(a²-b²)→化简
由a/b=3/2得,a=3b/2
∴(a²+b²)/(a²-b²)=【(3b/2)²+b²】/【(3b/2)²-b²】→代入a=3b/2
=【9b/4+b²】/【9b/4-b²】→化简
=【13b/4】/【5b/4】→化简
=13b/5b=13/5

a/b=3/2,求a/a+b + b/a-b
a/(a+b) + b/(a-b)(分子分母同时除以:b
=(a/b)/(a/b+b/b)+(b/b)/(a/b-b/b)
=(a/b)/(a/b+1)+1/(a/b-1)
=(3/2)/(3/2+1)+1/(3/2-1)
=(3/2)/(5/2)+1/(1/2)
=3/2*2/5+2
=3/5+2
=13/5

是13/5吗
第一个式子可以得到a=多少多少b
要求的那个式子要化成相除的形式 这样b可以约掉
后面那个式子把底都化成(a+B)(a-b) 然后合到一个式子就行

a=3b/2
原式=(3b/2)/(3b/2+b)+b/(3b/2-b)
=(3b/2)/(5b/2)+b/(b/2)
=3/5+2
=13/5