<s>[INST] Simplify $\large{\frac{7x}{2x-1} +\frac{5x-2}{2x+2}}$ Simplify the rational expression.
$$\frac{7x}{2x-1} + \frac{5x-2}{2x+2}$$
My work:
\begin{eqnarray*} \frac{7x}{2x-1} + \frac{5x-2}{2x+2}
&=& \frac{7x(2x+2)+(5x-2)(2x-1)}{(2x-1)(2x+2)} \\ &=& \frac{7x(2x+2)+(5x-2)(2x-1)}{(2x-1)(2x+2)}.\end{eqnarray*}
Is this correct?
 [/INST] I think that it's more simple:
$$\frac{7x}{2x-1} + \frac{5x-2}{2x+2} = \frac72 + \frac{7x - \frac72(2x-1)}{2x-1} + \frac52 + \frac{5x-2-\frac52(2x+2)}{2x+2}=\\=
6 + \frac{7/2}{2x-1} + \frac{-7}{2x+2} = 6+\frac72\left(\frac{1}{2x-1}-\frac{1}{x+1}\right).
$$
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