Section 1.2 Precalculus Review

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Section 1.2 Precalculus Review

1. Simplify the expression

$\frac{x^{2} + x - 30}{x^{2} - 36}$

2. Simplify the expression

$\frac{150 t^{2} + 60 t + 6}{25 t^{2} - 1}$

3. Simplify the expression

$\frac{x^{3} + 7 x^{2} - 8 x}{- 7 x^{2} - x + 8}$

4. Simplify the expression

$\frac{{(1 + x^{2})}^{2} (2) - 3 x (2) (1 + x^{2}) (3 x)}{{(1 + x^{2})}^{4}}$

5. Simplify the expression

$\frac{x^{2} - 18 x + 81}{x^{2} - 4 x - 45} \cdot \frac{9 x + 45}{5 x^{2} - 48 x + 27}$

6. Simplify the expression

$\frac{5 x^{2} + 4 x - 1}{2 x + 6} \cdot \frac{x^{2} - 1}{x^{2} + 2 x - 3}$

7 Perform the indicated operations and simplify the expression

$\frac{33}{2 (2 t + 5)} + \frac{1}{2}$

8. Perform the indicated operations and simplify the expression

$\frac{3 x}{3 x - 1} - \frac{4 x}{3 x + 7}$

9. Perform the indicated operations and simplify the expression

$\frac{3}{x^{2} - 9} - \frac{4}{x^{2} - 6 x + 9}$

10. Perform the indicated operations and simplify the expression

$\frac{1 + \frac{3}{x}}{1 - \frac{3}{x}}$

11. Perform the indicated operations and simplify the expression

$\frac{\frac{1}{x} + \frac{1}{y}}{1 - \frac{8}{x y}}$

12. Perform the indicated operations and simplify the expression

\frac{12 x^{2}}{6 \sqrt{2 x^{2} + 9}} + \sqrt{2 x^{2} + 9}

13. Perform the indicated operations and simplify the expression

$6 {(3 x + 1)}^{2} \sqrt{x}$ ²+x + (3x+1)⁴4x²+x

14. Perform the indicated operations and simplify the expression

$\frac{4 x {(x + 4)}^{- \frac{1}{2}} - {(x + 4)}^{\frac{1}{2}}}{x^{2}}$

15. Perform the indicated operations and simplify the expression

$\frac{{(x^{2} - 1)}^{\frac{1}{2}} - 7 x^{2} {(x^{2} + 1)}^{- \frac{1}{2}}}{1 - 6 x^{2}}$

16, Perform the indicated operations and simplify the expression

$\frac{{(3 x + 2)}^{\frac{1}{2}} - (x + 9) {(3 x + 2)}^{- \frac{1}{2}}}{3 x + 2}$

17. Find the values of x that satisfy the inequalities. Enter your answer using interval notation

$- 9 < x - 5 < 8$

18. Find the values of x that satisfy the inequality

$- 4 \leq + 18 \leq 25$

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This question is taken from Math 238 – Calculus for Business and Social Sciences » Summer 2022 » Homeworks

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