91Ó°ÊÓ

Felipe thinks \(\frac{1}{x}+\frac{1}{y}\) is \(\frac{2}{x+y}\). Choose numerical values for \(x\) and \(y\) and evaluate \(\frac{1}{x}+\frac{1}{y}\). Evaluate \(\frac{2}{x+y}\) for the same values of \(x\) and \(y\) you used in part (a). (c) Explain why Felipe is wrong. (d) Find the correct expression for \(\frac{1}{x}+\frac{1}{y}\).

Simplify the expression \(\frac{4}{n^{2}+6 n+9}-\frac{1}{n^{2}-9}\) and explain all your steps.

Simplify each complex rational expression by writing it as division. $$\frac{\frac{2 a}{a+4}}{\frac{4 a^{2}}{a^{2}-16}}$$

Simplify each complex rational expression by writing it as division. $$\frac{\frac{3 b}{b-5}}{\frac{b^{2}}{b^{2}-25}}$$

Simplify each complex rational expression by writing it as division. $$\frac{\frac{5}{c^{2}+5 c-14}}{\frac{10}{c+7}}$$

Simplify each complex rational expression by writing it as division. $$\frac{\frac{8}{d^{2}+9 d+18}}{\frac{12}{d+6}}$$

Simplify each complex rational expression by writing it as division. $$\frac{\frac{1}{2}+\frac{5}{6}}{\frac{2}{3}+\frac{7}{9}}$$

Simplify each complex rational expression by writing it as division. $$\frac{\frac{1}{2}+\frac{3}{4}}{\frac{3}{5}+\frac{7}{10}}$$

Simplify each complex rational expression by writing it as division. $$\frac{\frac{2}{3}-\frac{1}{9}}{\frac{3}{4}+\frac{5}{6}}$$

Simplify each complex rational expression by writing it as division. $$\frac{\frac{1}{2}-\frac{1}{6}}{\frac{2}{3}+\frac{3}{4}}$$