Section P.7 Homework

1.  Find the domain of the expression.  −x⁴ + x³ + 6x

2.  Find the domain of the expression.

$\frac{5t^2–2}{6t+24}$

3.  Find the domain of the expression.

$\frac{1}{\sqrt{x–3}}$

4.  Simplify the rational expression.

$\frac{x^2–x–2}{x^2–1}$

5.  Simplify the rational expression.

$\frac{y^2–4y–12}{4y^2+11y+6}$

6. Perform the multiplication or division and simplify.

$\frac{x^2+x–6}{x^2–x–6}·\frac{3–x}{3+x}$

7.  Perform the multiplication or division and simplify.

$\frac{x+4}{25x^2–16}÷\frac{x^2+6x+8}{5x^2+11x–12}$

8.  Perform the multiplication or division and simplify.

$\frac{x/y}{z}$

9.  Perform the addition or subtraction and simplify.

$\frac{1}{x+9}÷\frac{5}{x–8}$

10.   Perform the addition or subtraction and simplify.

$\frac{5}{2x–3}–\frac{3}{{\left(2x–3\right)}^2}$

11. Simplify the compound fractional expression.

$\frac{1–{\displaystyle \frac{2}{y}}}{{\displaystyle \frac{9}{y}}–1}$

12.  Simplify the compound fractional expression.

$\frac{{\displaystyle \frac{1}{x–1}}+{\displaystyle \frac{1}{x+5}}}{x+2}$

13.  Simplify the expression. (This type of expression arises in calculus when using the “quotient rule.”)

$\frac{3{\left(x+1\right)}^2{\left(x–10\right)}^2–{\left(x+1\right)}^3\left(2\right)\left(x–10\right)}{{\left(x–10\right)}^4}$

14.  Rationalize the denominator.

$\frac{1}{4–\sqrt{2}}$

15.  Rationalize the denominator.

$\frac{2\left(x–y\right)}{\sqrt{x}–\sqrt{y}}$

16. Consider the expression

(a) How many terms does this expression have?

(b) Find the least common denominator of all the terms.

(c) Perform the addition and simplify.

17.   Find the domain of the expression.

$\frac{x^2+8}{x^2–7x–8}$

18.   Find the domain of the expression.

$\frac{\sqrt{4x}}{x+4}$

19.  Simplify the rational expression.

$\frac{x^2–3x–40}{x^2+9x+20}$

20.  Simplify the rational expression.

$\frac{4–x^2}{x^3–8}$

21.  Perform the addition or subtraction and simplify.

$\frac{x}{x^2+x–2}–\frac{6}{x^2–5x+4}$

22.   Rationalize the denominator.

$\frac{5}{2–\sqrt{5}}$

23   Rationalize the numerator.

$\sqrt{x^2+6}–x$