<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] You would also have to check that nothing cancels from FOILing the quadratics.
Is $\frac{24x^2+5x+2}{4x^2+2x-2}$ simplifiable?
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