$$w = \frac{(ab - d) }{c - a - b}$$(adsbygoogle = window.adsbygoogle || []).push({});

I have to solve the above equation for variables `c` and `d` if `w` can be any number from $$w \in (-\infty, +\infty)$$

If we set `w = 0, then w = 1` we can solve for `c and d`

$$0 = ab - d$$

$$d = ab$$

$$c = a + b$$

Now if I can substitute the values to check the solution for `w = 1`

$$c - a - b = ab - d$$

Substituting c, $$a + b - a - b = ab - d$$

$$0 = ab - d$$

$$d = ab$$

I know that my solution is true for both `w = 0 and w = 1` but how can I prove that my solution is true for $$w \in (-\infty, +\infty)$$

I've tried this:

$$w(c - a - b) = (ab - d)$$

$$w(a + b - a -b) = ab - d$$

$$0 = ab - d$$

$$ab = d$$

But is this really an acceptable way of solving the solution? I am very confused. I've proved that the equations I found earlier (when I set w = 1 and w = 0) are true when w = w by putting it into the mother equation

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# How can I find a solution for c and d for all real integer values?

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