91Ó°ÊÓ

Explain why \(\frac{4+3}{2+5}\) is not equal to \(\frac{4}{2}+\frac{3}{5}\).

Find the quotient and the remainder. Check your work by verifying that Quotient \(\cdot\) Divisor \(+\) Remainder \(=\) Dividend $$ x^{5}-a^{5} \text { divided by } x-a $$

Find the value of each expression if \(x=2\) and \(y=-1\) \(\sqrt{x^{2}}+\sqrt{y^{2}}\)

Expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and radicals appear. $$\frac{\sqrt[3]{8 x+1}}{3 \sqrt[3]{(x-2)^{2}}}+\frac{\sqrt[3]{x-2}}{24 \sqrt[3]{(8 x+1)^{2}}} \quad x \neq 2, x \neq-\frac{1}{8}$$

Expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and radicals appear. $$\frac{\sqrt{1+x}-x \cdot \frac{1}{2 \sqrt{1+x}}}{1+x} \quad x>-1$$

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime. $$ 16 x^{2}+24 x+9 $$

Find the value of each expression if \(x=2\) and \(y=-1\) \(x^{y}\)

Expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and radicals appear. $$\frac{\sqrt{x^{2}+1}-x \cdot \frac{2 x}{2 \sqrt{x^{2}+1}}}{x^{2}+1}$$

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime. $$ 9 x^{2}-24 x+16 $$

Find the value of each expression if \(x=2\) and \(y=-1\) \(y^{x}\)