State the sum in simplest form. \( \frac{4 x}{x-1}+\frac{2}{(x-1)^{2}}=\square \) Basic Funcs Trig Question Help: \( \square \) Mess

To combine the fractions, you'll need a common denominator, which is \((x-1)^{2}\). Rewrite the first term: \(\frac{4x}{x-1} = \frac{4x(x-1)}{(x-1)^{2}} = \frac{4x^{2}-4x}{(x-1)^{2}}.\) Now, you can add the fractions: \(\frac{4x^{2}-4x + 2}{(x-1)^{2}} = \frac{4x^{2}-4x + 2}{(x-1)^{2}}.\) Thus, the sum in simplest form is: \(\frac{4x^{2}-4x + 2}{(x-1)^{2}}.\) Take a step back and double-check your algebra! When adding fractions, it’s easy to misplace terms or add incorrectly. Keep a close eye on signs especially when combining like terms; one small mistake can throw off your entire calculation!