91Ó°ÊÓ

Fill in the blanks. The polynomials \(x-3\) and \(3-x\) are ____.

Fill in the blanks. The ________ common denominator of \(\frac{x-8}{x+6}\) and \(\frac{6-5 x}{x}\) is \(x(x+6)\).

A __________ is a mathematical statement that two ratios or two rates are equal.

Fill in the blanks. Method 1: To simplify a complex fraction, write its numerator and denominator as _________________ rational expressions. Then perform the indicated ____________ by multiplying the numerator of the complex fraction by the _____________ of the denominator.

Fill in the blanks. To ___________ a rational equation of fractions, multiply both sides by the LCD of all rational expressions in the equation.

Fill in the blanks. To _________ a rational expression, we multiply it by a form of \(1 .\) For example: \(\frac{2}{n^{2}} \cdot \frac{8 n}{8 n}=\frac{16 n}{8 n^{3}}\).

Fill in the blanks. a. To multiply rational expressions, multiply their ______ and multiply their ______. To divide two rational expressions, multiply the first by ______ of the second. In symbols, b. \(\frac{A}{B} \cdot \frac{C}{D}=\) and \(\quad \frac{A}{B} \div \frac{C}{D}=\frac{A}{B} \cdot\)

Choose the equation that can be used to solve the following problem: If the same number is added to the numerator and the denominator of the fraction \(\frac{5}{8},\) the result is \(\frac{2}{3} .\) Find the number. (i) \(\frac{5}{8}+x=\frac{2}{3}\) (ii) \(\frac{5+x}{8}=\frac{2}{3}\) (iii) \(\frac{5+x}{8+x}=\frac{2}{3}\) (iv) \(\frac{5}{8}=\frac{2+x}{3+x}\)

Fill in the blanks. Because of the division by \(0,\) the expression \(\frac{8}{0}\) is ____.

Write each denominator in factored form. a. \(\frac{x+1}{20 x^{2}}\) b. \(\frac{3 x^{2}-4}{x^{2}+4 x-12}\)