Question

simplify please help

Answer 1

$( {x}^{2} - x) - \frac{1}{2} ( x - 5 {x}^{2} + 3) \\ \\ = {x}^{2} - x - \frac{1}{2} \times x - \frac{1}{2} \times ( - 5 {x}^{2} ) - \frac{1}{2} \times 3 \\ \\ = {x}^{2} - x - \frac{x}{2} + \frac{5 {x}^{2} }{2} - \frac{3}{2} \\ \\ = {x}^{2} + \frac{5 {x}^{2} }{2} - x - \frac{x}{2} - \frac{3}{2} \\ \\ = (1 + \frac{5}{2} ) {x}^{2} - x(1 + \frac{1}{2}) - \frac{3}{2} \\ \\ = ( \frac{2+5}{2} ) {x}^{2} - x( \frac{2+1}{2}) - \frac{3}{2}\\ \\ = \frac{7}{2} {x}^{2} - \frac{3}{2} x - \frac{3}{2} \\ \\ = \frac{1}{2} (7 {x}^{2} - 3x - 3)$

Answer 2

Step-by-step explanation:

$\begin{lgathered}( {x}^{2} - x) - \frac{1}{2} ( x - 5 {x}^{2} + 3) \\ \\ \\ = {x}^{2} - x - \frac{1}{2} \times x - \frac{1}{2} \times ( - 5 {x}^{2} ) - \frac{1}{2} \times 3 \\ \\ \\ = {x}^{2} - x - \frac{x}{2} + \frac{5 {x}^{2} }{2} - \frac{3}{2} \\ \\ \\ = {x}^{2} + \frac{5 {x}^{2} }{2} - x - \frac{x}{2} - \frac{3}{2} \\ \\ \\ = (1 + \frac{5}{2} ) {x}^{2} - x(1 + \frac{1}{2}) - \frac{3}{2} \\ \\ \\ = ( \frac{2+5}{2} ) {x}^{2} - x( \frac{2+1}{2}) - \frac{3}{2}\\ \\ \\ = \frac{7}{2} {x}^{2} - \frac{3}{2} x - \frac{3}{2} \\ \\ \\ = \frac{1}{2} (7 {x}^{2} - 3x - 3)\end{lgathered}$