數學問題(回答要清和明)

1)4x = 3y當 x = y = 0 , x/y = 0/0 沒有意義。當 x , y ≠ 0 , 才有 x/y = 3/4。

2)2x - y/3 = 6 .....(1)
x + y/6 = -1 .....(2)(1) + 2*(2) :2x - y/3 + 2x + y/3 = 6 - 2
4x = 4
x = 1

3)a : b = 2 : 3 , b : c = 4 : 3==>
a : b = (2 : 3) * (4 : 4) , b : c = (4 : 3) * (3 : 3)==>
a : b = (8 : 12) , b : c = (12 : 9)==>
a : b : c = 8 : 12 : 9;(a - b + c) / (a + b - 2c)= (8 - 12 + 9) / (8 + 12 - 2*9)= 5 / 2

4)√b / (√a-√b) - √a / (√a+√b)= √b (√a+√b) / ((√a-√b)(√a+√b)) - √a (√a-√b) / ((√a+√b)(√a-√b))= (√(ab) + b) / (a - b) - (a - √(ab)) / (a - b) = (2√(ab) + b - a) / (a - b)= 2√(ab) / (a - b) - 1

5)1 / (2x - x²) - 1 / (x² + x - 6)= 1 / (x(2 - x)) - 1 / ( (x - 2)(x + 3) )= 1/(x - 2) * ( - 1/x - 1/(x + 3) )= 1/(x - 2) * ( (-(x+3) - x) / (x(x+3)) )= 1/(x - 2) * ( - (2x+3) / (x(x+3)) )= - (2x+3) / ( x (x-2) (x+3) )