how can i change the subject of the formula a+b/x-y = a-b/x+y into y?
thanks!
(the answer is y= -bx/a)
A question
2006-11-12 11:51 pm
回答 (3)
2006-11-12 11:56 pm
✔ 最佳答案
a+b/x-y = a-b/x+y(a+b)(x+y) = (x-y)(a-b)
a(x+y) + b(x+y) = x(a-b) - y(a-b)
ax+ay+bx+by = ax-bx-ay+by
ay+by+ay-by = ax-bx-ax-bx
y(a+b+a-b) = -2bx
y(2a) = -2bx
y = -bx/y
2006-11-12 15:58:11 補充：
小小提示：要轉 subject，如有需要，首先要 expand 開o的 terms.. 再 group 埋你需要o既 element（在你的題目是 y）﹐那麼就可以。
2006-11-13 12:05 am
(a+b)/(x-y) = (a-b)/(x+y)
(a+b) (x+y) = (a-b) (x-y)
ax+ay+bx+by = ax-ay-bx+by
ay+by+ay-by = ax-bx-ax-bx
2ay = -2bx
ay = -bx
y = -bx/a
(a+b) (x+y) = (a-b) (x-y)
ax+ay+bx+by = ax-ay-bx+by
ay+by+ay-by = ax-bx-ax-bx
2ay = -2bx
ay = -bx
y = -bx/a
2006-11-12 11:57 pm
主項變換 (change of subject)
a+b/x-y = a - b/x+y 【y】
(a+b)(x+y) = (a - b)(x - y)
ax+ay+bx+by = ax - ay - bx+by
ay+by+ay - by = ax- bx - ax - bx
2ay = -2bx
y = -2bx / 2a
y = -bx/a
2006-11-12 16:06:36 補充：
由第一部跳到第二部，因為兩邊都是分數所以將分母乘上去，即「交叉相乘」a b / x﹣y = a﹣b/x y 【y】(a＋b)(x＋y) = (a﹣b)(x﹣y)ay by ay - by = ax- bx - ax - bx2ay = -2bx ←處理同類項加減變成，之後計到答案
a+b/x-y = a - b/x+y 【y】
(a+b)(x+y) = (a - b)(x - y)
ax+ay+bx+by = ax - ay - bx+by
ay+by+ay - by = ax- bx - ax - bx
2ay = -2bx
y = -2bx / 2a
y = -bx/a
2006-11-12 16:06:36 補充：
由第一部跳到第二部，因為兩邊都是分數所以將分母乘上去，即「交叉相乘」a b / x﹣y = a﹣b/x y 【y】(a＋b)(x＋y) = (a﹣b)(x﹣y)ay by ay - by = ax- bx - ax - bx2ay = -2bx ←處理同類項加減變成，之後計到答案
參考: the form two maths book
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