# Are these two equation equivalent?

During macroeconomics we have computed the algebraic IS-LM equilibrium. Unfortunately the final result we found during class differs from the result written on our Macroeconomics book. This is what we found in class: $$Y=\frac{d_2}{f_2 + \frac{d_2f_1}{1-c_1-d_1}} \cdot \frac{M}{P}+\frac{1}{(1-c_1-d_1)+\frac{f_1}{f_2} \cdot d_2} \cdot A$$

And this is the equation written on the book: $$Y=\frac{1}{(1-c_1-d_1)\frac{f_2}{d_2}+f_1} \cdot \frac{M}{P}+\frac{1}{(1-c_1-d_1)+\frac{f_1}{f_2} \cdot d_2} \cdot A$$

As you can see the part which multiplies A is equal in both equations, but the first part isn't. My question is: are the two equation equivalent or they differs?

No, it seems to me that the denominator $1-c_1-d_1$ is missing.If you start from the first formula and you divide out by $d_2$, everything is alright. But you are in trouble when you multiply by $1-c_1-d_1$, since the final result should be $$\frac{1-c_1-d_1}{(1-c_1-d_1)\frac{f_2}{d_2}+f_1}.$$