1)) Divide . Write your answer in simplest form. (3w^2-5w+2)/(4w^2)+11w-3div (w^2-2w+1) square

To divide the given expression, we need to multiply the first fraction by the reciprocal of the second fraction.<br /><br />The reciprocal of $(w^{2}-2w+1)$ is $\frac{1}{w^{2}-2w+1}$.<br /><br />So, the expression becomes:<br /><br />$\frac{3w^{2}-5w+2}{4w^{2}+11w-3} \times \frac{1}{w^{2}-2w+1}$<br /><br />Now, let's simplify the expression:<br /><br />$\frac{3w^{2}-5w+2}{4w^{2}+11w-3} \times \frac{1}{w^{2}-2w+1} = \frac{3w^{2}-5w+2}{(4w^{2}+11w-3)(w^{2}-2w+1)}$<br /><br />To simplify further, we can factorize the numerator and denominator:<br /><br />$\frac{3w^{2}-5w+2}{(4w^{2}+11w-3)(w^{2}-2w+1)} = \frac{(3w-2)(w-1)}{(4w-1)(w+3)(w-1)}$<br /><br />Now, we can cancel out the common factors in the numerator and denominator:<br /><br />$\frac{(3w-2)(w-1)}{(4w-1)(w+3)(w-1)} = \frac{3w-2}{(4w-1)(w+3)}$<br /><br />Therefore, the simplified form of the given expression is:<br /><br />$\frac{3w-2}{(4w-1)(w+3)}$<br /><br />So, the answer is $\frac{3w-2}{(4w-1)(w+3)}$.