91Ó°ÊÓ

After finding the simplest form of each fraction, explain why it cannot be simplified more. (a) \(\frac{x^{3}-x}{1-x}\) (b) \(\frac{2 x^{2}+4 x}{2 x^{2}+4}\)

Perform the indicated operations. Each expression occurs in the indicated area of application. $$\frac{a}{b^{2} h}+\frac{c}{b h^{2}}-\frac{1}{6 b h} \text { (strength of materials) }$$

Answer the given questions. If \(3-x<0,\) is \(\frac{x^{2}-9}{3-x}>0 ?\)

Solve the given problems. Find the two integer values of \(k\) that make \(4 x^{2}+k x+9\) a perfect square trinomial.

Perform the indicated operations. Each expression occurs in the indicated area of application. $$\frac{\frac{L}{C}+\frac{R}{s C}}{s L+R+\frac{1}{s C}} \text { (electronics) }$$

Answer the given questions. If \(x-4<0,\) is \(\frac{x^{2}-16}{x^{3}+64}<0 ?\)

Perform the indicated operations. Each expression occurs in the indicated area of application. $$\frac{\frac{m}{c}}{1-\frac{p^{2}}{c^{2}}} \text { (airfoil design) }$$

Factor the expressions completely. In Exercises 73 and \(74,\) it is necessary to set up the proper expression. Each expression comes from the technical area indicated. \(4 d^{2} D^{2}-4 d^{3} D-d^{4} \quad\) (machine design)

Solve the given problems. Find the two integer values of \(k\) that make \(16 y^{2}+k y+25\) a perfect square trinomial.

Solve the given problems. Find six values of \(k\) such that \(x^{2}+k x+18\) can be factored.