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Chapter 7: Problem 77

Explain how to multiply rational expressions.

Short Answer

Expert verified
To multiply rational expressions, break down the expressions, multiply the numerically similar parts (numerators and denominators) then simplify the result.

Step by step solution

01

Breaking down the Rational Expressions

Break down both the numerator and the denominator of the rational expressions into their simplest forms. This involves factoring the polynomials in the numerator and the denominator, splitting them into terms that when multiplied back together will form the original expressions.
02

Multiplying the Rational Expressions

After breaking down the expressions, multiply the numerators with each other to get a new numerator, and the denominators with each other to get a new denominator. Remember the basic rule of fractions: \(\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\). Apply this rule to your expressions.
03

Simplifying the Result

Once you鈥檝e multiplied out your rational expressions, further simplify the result if it鈥檚 possible. This might involve factoring the numerator and denominator again, and canceling out any common factors between them or simplifying any like terms within either the numerator or denominator.

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Most popular questions from this chapter

Exercises \(123-125\) will help you prepare for the material covered in the next section. a. Add: \(\frac{1}{3}+\frac{2}{5}\) b. Subtract: \(\frac{2}{5}-\frac{1}{3}\) c. Use your answers from parts (a) and (b) to find \(\left(\frac{1}{3}+\frac{2}{5}\right) \div\left(\frac{2}{5}-\frac{1}{3}\right)\)

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3 x}{x^{2}-y^{2}}-\frac{2}{y-x}$$

Exercises \(123-125\) will help you prepare for the material covered in the next section. Multiply and simplify: \(\quad x y\left(\frac{1}{x}+\frac{1}{y}\right)\)

Multiply: \(\quad(3 x+5)(2 x-7)\).

Perform the indicated operation or operations. Simplify the result, if possible. $$\frac{3}{x^{2}+4 x y+3 y^{2}}-\frac{5}{x^{2}-2 x y-3 y^{2}}+\frac{2}{x^{2}-9 y^{2}}$$
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