Fraction Equals c/d

When x is added to both the numerator and the denominator of the fraction a/b, where a and b are both not equal to 0, the value of the fraction is changed to c/d. Then what is x?

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a + x  =  c
b + x d

d(a + x) = c(b + x)
ad + dx = bc + cx
dxcx = bcad
x(dc) = bcad

x bcad  =  adbc
dc cd

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