Help with this multiple choice maths

Question

If a/b + c/d = a+c/b+d , where a,b,c and d are non zero integers and b+d is NOT 0, then

- one of a and c is positive and the other is negative

- a and c are both even

- b and d are equal

- b and d have a common factor

- there are no values of a b c and d for which this is true

Answer 1

Liz, here is how to attack this problem:

First, convert (a/b)+(c/d) to a fraction. Call it X.

Second, you have an equation with X on one side and (a+c)/(b+d) on the other side. Cross multiply the numerators and denominators to make an equation with no denominators.

Third, we are in luck! One side contains nothing but (abd + bcd), while the other side has the same terms and a few others. So, after subtracting the equal terms from both sides, we are with Zero on one side and exactly two terms on the other, each of which has a square.

 

when you perform the steps I just outlined, you’ll be closer to seeing how to get the answer. For each one of the multiple choices, ask yourself “would this condition make it possible for that sum to be equal to zero?”

 

try it and see, if you still have questions, please ask again.