Question

`(x^(2) -1)/(16x) X (4x^(2) )/(5x + 5)`

Answer 1

x^2-x / 20

Explanation:

Answer 2

`\underline{\underline{\large\bf{Solution:-}}}\\`

`\begin{gathered}\\\implies\quad \sf (x^(2) -1)/(16x) * (4x^(2) )/(5x + 5) \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf \frac{\cancel{(x+1)}(x-1)}{16x} * \frac{4x^(2) }{5\cancel{(x + 1)}} \quad\quad(a^2-b^2 = (a+b)(a-b))\\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf \frac{x-1}{\cancel{16x}} * (\cancel4x^(\cancel2) )/(5) \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf ((x -1)(x))/(4* 5) \\\end{gathered}`

`\begin{gathered}\\\implies\quad \sf (x^2-x)/(20) \\\end{gathered}`

More Identities:-

`\begin{gathered}\boxed{\sf{ {(a + b)}^(2) = {a}^(2) + {b}^(2) + 2ab \: }} \\ \end{gathered}`

`\begin{gathered}\boxed{\sf{ {(a - b)}^(2) = {a}^(2) + {b}^(2) -2ab \: }} \\ \end{gathered}`

`\begin{gathered}\boxed{\sf{ {x}^(2) - {y}^(2) = (x + y)(x - y) \: }} \\ \end{gathered}`

`\begin{gathered}\boxed{\sf {(a + b)² = (a - b)² + 4ab\: }} \\ \end{gathered}`

`\begin{gathered}\boxed{\sf {(a - b)² = (a + b)² - 4ab\: }} \\ \end{gathered}`

`\begin{gathered}\boxed{\sf {(a + b)² + (a - b)² = 2(a² + b²)\: }} \\ \end{gathered}`

`\begin{gathered}\boxed{\sf{ (a + b)³ = a³ + b³ + 3ab(a + b)\: }} \\ \end{gathered}`

`\begin{gathered}\boxed{\sf {(a - b)³ = a³ - b³ - 3ab(a - b)\: }} \\ \end{gathered}`