A fraction problem a = x + 1 x b = y + 1 y...
A fraction problem
Express in terms of and
Answer & Explanation
Note that is not uniquely specified by and , since solving for yields two solutions which are reciprocals of each other, and applying or to yields . However, applying either substitution again gives back , so can take on either of those values.
Let and . One can check that
Use the quadratic formula to solve for the possible values of
Multiply all things by the LCD to remove fractions.
Multiply the first two equations to get
Adding the first two equations, we get
Combining these two lines,
At this point, I'd just go back and solve for using the quadratic formula,
Not the most beautiful thing in the world, but at least you don't have to square the thing or anything messy like that.