Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.6 - Page 87: 71

$\frac{-(2x+h)}{x^{2}(x+h)^{2}}; x \ne 0,-h; h\ne 0;$

Work Step by Step

Given Expression, $\frac{\frac{1}{(x+h)^{2}} - \frac{1}{x^{2}}}{h}$ Taking LCD in the numerator, $= \frac{\frac{x^{2}-(x+h)^{2}}{(x+h)^{2}x^{2}}}{h}; x \ne 0,-h; h\ne 0;$ Using $[(a+b)^{2} = a^{2} + 2ab +b^{2}; (x+h)^{2} = x^{2} + 2xh +h^{2}]$ $= \frac{\frac{x^{2}-(x^{2}+2xh+h^{2})}{(x+h)^{2}x^{2}}}{h}; x \ne 0,-h; h\ne 0;$ $= \frac{\frac{x^{2}-x^{2}-2xh-h^{2}}{(x+h)^{2}x^{2}}}{h}; x \ne 0,-h; h\ne 0;$ $= \frac{\frac{-2xh-h^{2}}{(x+h)^{2}x^{2}}}{h}; x \ne 0,-h; h\ne 0;$ $= \frac{\frac{-h(2x+h)}{(x+h)^{2}x^{2}}}{h}; x \ne 0,-h; h\ne 0;$ $= \frac{-h(2x+h)}{(x+h)^{2}x^{2}} \times \frac{1}{h}; x \ne 0,-h; h\ne 0;$ Divide out common factors. $= \frac{-(2x+h)}{x^{2}(x+h)^{2}}; x \ne 0,-h; h\ne 0;$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.