Question

Suppose that a/c = b/d where a, b, c, and d
d are real numbers. Use both arithmetic and
algebra to show that a/c = a-b/c-d is true.

Answer 1

THEOREM.

If a/b=c/d then a/c=b/d

Solution.

a/b=c/d

a/b - 1=c/d - 1

a/b - b/b=c/d - d/d

(a-b) /b = (c-d)/d

(a-b) /(c-d) =b/d

In theorem b/d=a/c

(a-b) /(c-d) =a/c

The example is solved.